I did a quick spot check and a fair number of the ASOS/AWOS/ATIS frequencies in my area were 1xx.x25 or 1xx.x75. No problem with local Center, approach, or tower frequencies that I could see. I note that Rapid City (where the plane is now at) has ASOS on 118.525. If they couldn't tune to that they'd have to get the numbers from the tower. Not sure if they would hear anything on 118.500 or 118.550.My info is dated, but you may want to check into this further. I believe the FARs state you only require two-way communications with ATC on the appropriate frequencies. The AC is not regulatory. While you may not be able to use every airport or service due to lack of 25 khz spacing, I don't believe having a 360 channel radio prevents you flying IFR or entering controlled airspace.
The other thing is that the FCC outlawed transmission from the old radios that couldn't maintain frequency stability of 0.003% (the previous threshold was 0.005%) I found this article from 1996 that discusses the FCC regulatory issues that arose back then (and lists some of the radios that couldn't meet the new transmission tolerances):
https://www.aopa.org/news-and-media/all-news/1996/october/pilot/tuning-a-new-com