Spectral power density is the primary concern.

The legal power limit in these bands is 1 W. If you spread that out over 500 kHz, that signal is weaker than background noise at any given frequency for anyone more than about a city block away. (Give or take many factors.)

But, if you compress that 1 W into, say, 12.5 kHz (typical for FM voice), your signal is now detectable (and will interfere with other, possibly licensed, users) at over 6 times the distance.

There are probably other factors. For example, it's not legally sufficient to simply reduce your power by a corresponding factor. I suspect it may simply be the FCC's goal to reduce conflict between users by mandating spread-spectrum technologies for unlicensed use.

Note also that 47 CFR 15.247(e) [1] gives a spectral power limit which corresponds approximately with the 1 W max / 500 kHz min specified in (b)(3) and (a)(2).

Final side note – https://docs.fcc.gov/public/attachments/FCC-02-151A1.pdf is interesting reading as to how the current form of 15.247 came to be. Specifically it changed the rule from specifically DSSS to digital modulation generally, which in turn allowed the transition from 802.11b (DSSS) to 802.11g (OFDM) on 2.4 GHz.

[1] https://www.ecfr.gov/current/title-47/part-15/section-15.247...