Should I ask my students to contribute in preparation of the manuscripts?

When I did my masters, I had this problem. My old supervisor ended up rewriting a paper from scratch. He never really gave me any feedback except that my writing of the paper was not good and there is no way it will be accepted. I now understand that this approach was a waste of his time and a waste of a learning experience for me.

Now I am working with a different supervisor and when I write a paper, I get a lot of comments and feedback and we end up doing 4-5 rounds or review. I think the initial draft is usually not good. But after all these rounds of review, I end up writing a "good" paper myself.

Maybe your students need to realize that they have a problem that THEY need to address. You writing the papers on their behalf does not solve this problem. Initially, push them to write a draft regardless of quality. Then do rigorous review afterward. With time, their writing will definitely improve

This, as always, might be highly dependent on the field. So here's my opinion from a (synthetic) chemists point of view:

It's fine to let bachelor/master students contribute but I wouldn't let them write the (first) draft. For writing a good paper you need a lot of background knowledge, which especially bachelor students usually don't have, and a good knowledge about all the subtle details on how to write such papers. What we usually do is let them prepare the supporting information/experimental section where they write up their experiment and also figures (which is the most important part anyways) while the main part is written by experienced supervisors who can also do it in a fraction of the time. But we like to include the students so they get to know the whole process of writing such a paper.

We usually start letting students write their own manuscripts sometimes at the beginning of PhD using smaller projects and papers send to rather low impact journals (most of the time invited papers). After that it's usually fine to let them write first drafts of the more important papers and we never had anyone complaining or taking it badly even if we basically rewrote the whole thing.

They are going to be expected to have a level of writing skill upon graduation. If they don't have that, it can reflect poorly on your lab. It also harms them in the long run.

You said that they have difficulty with writing up their research and want to know how to motivate them.

I would point out that these are two different things. Difficulty writing a quality manuscript is understandable; professional writing is a skill which must be developed. In that case, I would patiently go through rounds of revision and be very strict in your reviewing (because other people will be). Then go over with them everything you marked and explain why you chose to change it. Be honest, but constructive. Don't say "this was stupid," say "I see what you were trying to say here, but what you say implies X, and we want to avoid that. If instead we say it this way, we avoid that implication entirely."

If the problem is not that they lack the skill but instead lack the desire to learn how to write professionally, then this is a different problem entirely. If this is the case, I would sit down with them and bluntly tell them that you aren't going to waste any more of your time on them until they make an effort, and that if they aren't willing to put in the work necessary to become a professional in your field, maybe they should be seeking elsewhere for their development.