My quick thoughts (albeit only "from the hip" in the sense that I am writing them in real time -- they are largely things I've thought about quite a bit over the years). Hopefully they're at least worth what you're paying for them.
First, it is important to distinguish whether what you're doing with any given song and recording is something you are doing as an "artist", something you're doing purely for commercial/business purposes, or somewhere in between (and where in the spectrum from one end to the other, if in between). What's the difference, and why does it matter?
When I say "as an artist", I mean something you're putting out because you have something to say and want to get out into the world, whether or not it ever makes any money. "Sharing" is more important than financial returns, and your involvement in it, on any applicable fronts (e.g. publishing, promotion, identity, creation), is something you want to maintain a level of control over. On this end of the spectrum, unless you're pretty much immediately finding someone "in the business" who is ready to invest in you in some way, and you're willing to give them what they want in return for that investment, it makes a lot of sense to get your stuff out there independently (assuming, of course, you believe it is good enough).
To gain financial success on this end, you will likely need to invest time and money in promoting yourself and your music. Otherwise it gets almost as few listens as the proverbial tree that falls in the forest with no one around to hear it, and the odds of making any significant money with what you're putting out there are extremely slim. That doesn't mean it can't happen, of course, and sometimes even small levels of exposure can get you into consideration for opportunities "by accident", and of course you can always pitch to opportunities you find and have access to. (For perspective, I've had my music on the internet in one way or another since the mid-90s, and just having a presence during those early days, and having quality songs, led to somewhere around a dozen indie cuts of those songs, probably at least an equal number of artists using my songs on their artist demos, and some single song publishing deals, though the publishing deals never ended up netting any cuts -- the cuts I got were ones I handled directly as a self-publisher. More recently, having my cover of "Time is on My Side" out there, via CD Baby distribution, led to being contacted by a music licensing professional who wanted to pitch it into a specific ad opportunity. While that didn't lead to a placement, it wouldn't have even been pitched had I not had the recording out there.)
I am 100% self-published at this point on my "artist" side, but, if a meaningful opportunity that made it worth signing publishing to someone else, it would be a pretty simple matter for me to update my ASCAP records to change the publisher assignment, terminate any CD Baby "monetize my music" settings for the song(s) in question, and remove it from my SongTradr catalog (where applicable). (FWIW, I don't use CD Baby Pro because the few additional things it does aren't leaving enough money on the table to warrant the cost.) In general, though, with respect to TAXI pitching, I typically only pitch material that is out this way to direct-to-music-supervisor (or equivalent) listings, artist song pitches, and non-exclusive library listings.
On the other end of the spectrum is creating purely for financial reasons -- essentially treating it as a day job where you may not be creating from something inside you but to meet a specific external need that at least holds some promise of a payoff. For me, this would largely cover trying to write for cues and/or other instrumental needs. In most cases, I'd be writing directly for a TAXI listing, which may or may not be exclusive. If it's cues, it is not something I'd ever put out as an artist. I have actually put out some of the instrumental songs I've written, but generally long after the TAXI return (or in one case years after a TAXI forward where I never heard back from whoever it was forwarded to). In general, though, this stuff is the "write, submit, forget, repeat" stuff. While I do my best on any given creation of this sort, I also recognize that this is essentially "disposable" music in the sense that there are lots of people out there creating it, at various quality levels, and it's not the kind of stuff that is truly unique to me in any meaningful way. It's not the sort of thing that would become a hit song, even if it got a huge placement. It's really meant as background for visuals.
In this case, it seems to me to make sense to not be too precious about any individual piece, or even a collection of pieces. Once I've pitched a piece for a listing and gotten a return, I might put it up in something like SongTradr to allow for sync opportunities (and even to pitch to listed opportunities). If I were trying to be an instrumental composer as a mainline thing (I am not), I'd probably put some of this stuff up on my website. But it's not stuff I'd put out on streaming services for any sort of monetization. Or, if the nature of it was such that that made sense (e.g. I know a guy who put out some piano meditation music and even a collection of "soothing ringtones" and made some good money off that stuff during the heyday of download sales), then it wouldn't likely be among the material I'd be submitting to TAXI listings (unless perhaps non-exclusive ones). It is the "write, submit, forget, repeat" stuff that I'd be submitting, at least until I was certain it wasn't going to gain any traction that way but was still worth putting out in some other way.
Between these polar extremes would be territory like hoping to get more mileage out of something you're putting out into the world as an artist but might also be perfect for some specific sync placement, where the sync placement could also help get the work out to a wider audience. And writing for listings of this sort could also be situations where you are targeting the listing, but can also inject something you personally have to say into the work. A fair number of the songs I've written over the last decade actually started out this way, though I don't think any of those got forwarded. (One instrumental song did, but that was decidedly out of my mainstream, and I did it more as an experiment than anything else. Another instrumental that got rejected from its initial listing did actually get forwarded for another I submitted years later.) In these cases, I'll generally at least wait for a response to the listing. If it got forwarded, especially if it was an exclusive library listing, I'd likely hold the song back from putting out as an artist until some period of time had elapsed that made me feel like it wasn't likely to get signed. If it did get signed, then I'd have to take into account whatever parameters the specific deal allowed, such as if it was okay to release on my own (albeit without monetization options).
I guess what I'm getting at is it's important to honor your own specific reasons for doing all this, be aware of the business models and needs of the "customers" (e.g. libraries, traditional publishers, the public, etc.) you are targeting, then do whatever is in the best interests of meeting your specific goals. The "write, submit, forget, repeat" model won't be for everyone, it might be a subset of the overall body of work for some, and it may be the main model for others. What may be solid advice for one area may make little sense for another area. Writing for libraries is very different from trying to establish a presence (and make money) as an artist. In the latter case, while the music needs to be right for some audience, marketing takes on a great deal of importance because, in today's world, where there really aren't gatekeepers in the traditional music industry sense, it is about developing a fanbase and getting to a point where that fanbase wants to purchase something you have to offer, spread the word to others who might also be part of your potential audience, and otherwise support you.
Rick