I can see no reason why there should not be a comparative of the adjective ‘nice’ when used as meaning ‘pleasant or agreeable’; nor does the poster present one.
It may be that some linguistic pedants feel that because one of the earlier meanings of nice expressed the absolute idea of ‘precise, fine’, for which there was no comparison, this should carry over to other meanings. But that is not how languages work — new meaning, new usage.
There is ample evidence that ‘nicer’ has been in use since the 19th century — you just need to do a Google Books ngram search. Some examples:
Daisy, by Susan Bogert Warner, 1868
I think a vase of flowers would be a great deal nicer,” I said.
Oliver Beaumont and Lord Latimer, by Lady Emily Charlotte M. Ponsonby, 1873
“I mean that I think your plan as it is is so very nice, I would not try to make it nicer.”
I accept that the word ‘nice’ itself is weak in force, and an educated adult would use an alternative in many cases. In this respect it is interesting that both of these and some other 19th century examples are from children’s books, although they do not jar particularly. However if ‘nice’ is or was acceptable in this context, surely the comparative, ‘nicer’ should also be.
Even in its meaning as ‘precise, fine’, we find in the New England Journal of Dentistry for 1882
For if the impulse to development is given from without by the environment, these organs must be continually improved so as to perceive the nicer and nicer distinctions in the environment which will be the means of elevating the mind.
There seems to have been a decline in usage in the early 20th century (perhaps paralleling a discouragement of the use of ‘nice’), although
in 1920 Hilaire Belloc, very much tongue-in-cheek, used the superlative, ‘nicest’, in:
The nicest child I ever knew
Was Charles Augustus Fortescue.
But returning to ‘nicer’, more mundane examples can be found in the mid century:
Unemployment Compensation Interpretation Service: Benefit series, 1948
…she would be required to purchase new clothes of good quality suitable for sales work in one of the nicer places…
The poster asks “Has the language changed?”. Of course it has — although not on the timescale the question suggests for this particular case. Language changes continually. And certainly an examination of the ngram cited above shows a steep rise in use in the 21st century, in both British and American writing. Presumably it is considered ‘nicer’ than it once was.