Your objection seems to be: I can't move a component from a TW project to a non-TW project, and it would be difficult to combine a TW project and non-TW project. Is that a fair summary?
On the first point, moving a component from one project to another one that use a different CSS framework is sort of a weird thing to do. I've seen cases where people combine Bootstrap with a bunch of random personal styles, but I haven't seen anyone combine Bootstrap with e.g. Material design. ISTM if you're combining projects, you'll get a lot of CSS bloat and unexpected interactions.
On point two, you actually can tell TW to use a prefix, so instead of margin-left/right: auto being "mx-auto" it would be "prefix-mx-auto". Doing that would let you combine TW with another project that used the same class names (though obviously, you're going to have to go back and fix all the class names in an existing component).
TW's niche, ISTM, is for people who want to make small-ish, highly customized sites quickly. I don't you'll be happy with it if you need to integrate with a lot of legacy CSS. I also think if you don't really need custom styles, then you can just use Bootstrap/Material/Bulma/whatever and it will be much simpler than having to make all your buttons yourself or whatever. But for things like isolated landing pages, TW is great because you get an experience that is like writing a new CSS file, but quicker (no need to switch between the HTML and CSS or make up names) and better guided (preset variables for the sizes, colors, and breakpoints).