Now you're talking pineapples and string beans.
As far as routers, I agree manufacturers can be misleading. First, since most routers are dual-band concurrent (2.4 GHz and 5 GHz), manufacturers often add together the max bandwidths of each frequency and boast speeds of 1200, 1750 or 2600 Mbps. Second, as you noted, theoretical vs. real-world speeds are apples and oranges, but this mismatch is mostly about routers...not modems.
Modems, on the other hand, are only dependent on their technology: CDLP, Com21, DOCSIS, DVB/DAVIC, IEEE 802.14, IETF. Cox has nothing to do with a modem other than selling modems. It wouldn't matter if you bought the same make/model from Best Buy or Cox, it'd be the same modem with the same technology and the same capabilities. Are there bad makes/models? Absolutely but it'd have nothing to do with Cox but with the manufacturer.
The bandwidth of a plan depends on the technology of a modem. If OP wants 1 of the 3 highest plans, get a D3.1. If OP wants 1 of the 4 lower plans, get a D3.0. You should save your money with a lower plan because you wouldn't need a D3.1.
Even a D2.0 would still work on the Cox network and this would be okay if it's delivering the promised bandwidth of an Essential, Starter or Connect2Compete plan.
Mouth once noted Cox only wants D3.1 because it's more efficient on their network. Efficiency on their network wouldn't be my problem if I'm getting my promised bandwidth. For example, if I subscribe to Essential and still get my 40 Mbps, efficiency be damned.
My only problem...as well as your observation to troubleshoot...are the crappy routers Cox bolts onto the modems. Most of the time, the modems are fine. It's just the awful router attached to it.