I know persons who are doing this in times. A example is a person I am knowing who say "Mexico" with Spanish accent. A first problem is this person is not a speaker of Spanish and so it is bothering on me for bad pronounsing and no interests in improvement and not in learning more Spanish. A second problem is it disruptes conversation when a person is slipping into different accent without reasoning. A third problem is it takes persons I am knowing who are not speaker of Spanish extra time for to process these remarks. I am not seeing any good reason. There exists also a difference between nation name, is fixed, and brand, for which the job is make friendly for a consumer.
Yah. It can also sometimes be difficult to distinguish between an attempt to use the native pronunciation out of respect vs. mockery. I know people that if I heard them saying "Me-hi-co" it would almost certainly be to exaggerate foreignness and to be racist.