You say you understand, but your comment makes it sound as if you do not realize??
The issue of inner grooves is a cutting AND playback issue. You focus entirely on playback and try to paint a Rosy picture. The inner grooves are always compromised, during cutting also.
That is why the last song on most sides is always a ballad or quieter number. Most mastering engineers reduce the level a bit AND reduce the highs to get around this issue.
Any issue in playback, (such as inner groove distortion or roll off of highs) has a similar but opposite effect during cutting.
The grooves are packed tighter and tighter as there is far less "Real estate" to cut the "Groove" and consequently the radius is smaller and it becomes harder to cut AND playback towards the middle.
Part of the reason for 45 Rpm records with only a couple songs.
You really need to work with this stuff in order to understand how it works.
You're trying tell someone that owned a mastering operation and mastered LPs and who has done measurements on the cutting operation to insure its working, how it doesn't do what the measurements have shown it does. I'm going with the measurements on this one rather than accept myth on its face.
FWIW there are plenty of LPs that have quite a lot of modulation in the inner grooves. Your idea of 'quieter numbers' being placed near the label is mythological- record companies going all the way back to 1958 when Westerex released their original stereo cutter head (3D) paid no attention to this idea. Get a copy of RCA's Living Stereo Pines of Rome and you'll see what I mean.
My system was a Scully Lathe with Westerex 3d cutter and 1700 electronics. When I did the measurements of high frequencies, I was taking a lathe cut on a lacquer and placing it on the shop turntable (older SL1200 with Grado Gold) and playing it. Lacquers are softer than vinyl so you can appreciate that when I was able to play back 25KHz in the lead-out groove area, that an actual LP made of much harder vinyl will do so as well.
When going into this I had much the same opinion as you. That opinion died in the face of reality- figuring out how to operate the lathe was a painful experience (stupid mistakes burned few cutter voice coils which is something all new mastering engineers experience...) so the lessons it taught are hard won.
The Westerex system was old (I refurbished them)- the electronics were built in 1970 and designed earlier; the head was designed ten years earlier than that! Whatever the source you have, its simply incorrect, either from being out of date (as in the case of early and cheap phono cartridges) or is simply misinformation. It is a fairly common myth.