I guess you can see for yourself what the implications of copy-pasting design elements into another site are, it's pretty easy.
Use a technology that you can manipulate locally, like bootstrap. Make a page with it, and then create another site and design it as well. Now copy elements from one to the other. The HTML part is pretty easy. Now for the CSS, it's a bit harder to select only the CSS lines you need. Especially if there are inheritances and if the site don't have the same defaults. Once you've identified the minimum CSS to copy, where to copy it? At the beginning of the other site CSS file, or at the end? Or in the middle? What happens with all the redundancy classes? H1? H2? a? li? What gets prioritized, what gets not? Manually clean of add a prefix to all classes?
In the end, it's going to take you a lot of time and you'll have to make a lot of difficult decisions, just to end up with dirty HTML code and dirty CSS declarations. Dirty can only be a jugement because who care if it works? Well, some things are important, like accessibility. Accessibility means the code needs to be clear and understandable, hierarchies easy to understand, etc. If even you Hx are renamed, that's a code nightmare.
All this happens when you make decisions with your brain, difficult ones. So now imagine if a program has to make all those decisions... in order for that to work the program is not going to take any risk, it's gonna append all classes names and deal with hierarchy the best it can.
Me too I'd like to be able to speed up my work sometimes, and as I can imagine that Webflow could let us copy and paste structures of elements, complete HTML+CSS appears to me like a crazy thing to do. As an expert I will cringe a lot trying to help people who merged things multiple time, ending up in a total code disaster (read: I won't help). And even if I want to be able to duplicate structure, I can't see that happening because when less code savvy users will paste their structure it won't look good at all, and a large portion of uses aren't going to be able to deal with it at all. Because after pasting a structure you'll have to counteract the effect of the already defined styles that can conflict with the pasted structure, before styling them back into what is expected.
This is why I don't see this happening anytime soon.
Doing what you do now and having to recreate everything you've drafted elsewhere is actually GOOD. Because in the process you have the occasion to rethink you're structure, hierarchy of classes. That's called refactoring and when that happens it means good design or code quality.