Just a personal remark (that to some extent answers the question, for me personally). I usually have many things to do and am asked to review regularly, by several journals. I will strictly do reviews on a first come first serve basis. I will not be hassled by tight deadlines, and for sure a tighter deadline will not make me prioritise a review. Furthermore I decline as a matter of principle all requests that give me three weeks or less time, as this will not normally work according to the first come first serve rule.
More radically, as people know how busy everyone is, I think that if somebody sets a review deadline at less than three weeks, they implicitly communicate that they don't want a thorough high quality review, and consequently I won't review for them. This rules out reviewing for MDPI as far as I know them, but note that this is not exclusive to MDPI, and their reputation is not the issue here. However I'm not surprised in the least that they get crappy reviews given the time frame in which they're working.
I do know that high publication and reviewing speed is seen as desirable by many, and if somebody else is able to produce a good quality review in 10 days, fine by me. Still I value quality over speed, and quality takes time in my world.
Later addition: Once more not exclusive to MDPI, but... the problem with commercial publishers who use the model that the author and not the reader pays is that they have an economical incentive to accept papers. This will often play out as accepting papers more easily, and being generally more positive than critical reviewers, including potentially ignoring reject recommendations, although this will depend on the individual editor and journal. Some may be concerned enough about the scientific reputation of their journal to not accept all too bad stuff, others may accept far more than a competent and critical reviewer thinks they should.