I am in the dry cleaning camp. I find that dry cleaning is less harsh on the fabric (for example, I spot clean with water and stain remover any spots/stains and then take it to dry cleaner). I ask my dry cleaner to be gentle and just put it through the cleaning cycle without pressing it. I steam and press it myself thereafter (I use thin cheese cloth and iron on high from the back), also fix pulls, de-pile/de-fuzz, reround hems, etc - they look like new. But I don’t like them fluffy and fuzzy personally, so my goal is to maintain the appearance and a feel of a new shawl - or as close as possible to that original state.
As far as washing. I think it is ok to wash if you feel it is working for you. I would avoid washing vintage items as I have seen plenty of shawls with color running all around from being washed - so I would not be willing to risk that. Personal preference that is.
As far as corners when washing - it is normal for fabric to stretch when exposed to water, just need to reshape it and hopefully dry it flat to actually keep the shape…
As far as quality - it has changed significantly over the years - we noted it in previous discussions/ threads. Something from 1990/2000 will have a diff feel from early 2010 - and it started to get worse from then on. Some seasons were particularly bad (I avoid buying those seasons all together when shopping second hand