Do field research encounters always have worse stats each subsequent time you do the task?

No. It's totally random, within the stipulated IV range (10/10/10 to 15/15/15).

It's entirely random. Maybe your sample size is small? I've done thousands of research and most of the research mons I've kept came after lots and lots of tries.

Why on earth would Niantic implement such a pattern? This would have no purpose so I think they have better things to do and it's safe to assume it's not like that.

Same answer as to why some people seem to get more shinies than others: random is random is random. From research, you have a 1/216 chance of getting any specific IV spread. Given that so many more IV spreads are less than ideal it's easy to forget you're more likely to be given a bad hand than a good one.