Yeah, I like to compare it to the old "Party Line" phone lines people used to have, where you shared a single phone line with multiple houses and only one person could talk at a time. Sure, it gives you some of the functionality of a phone line, but it is not a phone line, and shouldn't be sold as the same thing.
Honestly, I'm genuinely surprised no ISP has started doing "gamer" marketing as it seems to be so effective elsewhere, "We give you real public IPs so you can connect directly to your opponents for lower latency, get on the internet fast lane!".
This already exists via VPNs that allegedly give you better routing/peering to the game servers.
No idea if they work. I can see conceptually why they might (internet routing is often more of an approximation of a best route than the actual best route), but the problems seem too individualized for a generic VPN to help. Happy to be wrong if someone knows how well/why they work.
A VPN isn't always an extra hop from a "hops in traceroute" perspective. It's very possible to get a shitty route from your ISP; e.g. if the best route goes through an ISP that your ISP has shitty peering with. You might get better latency via a VPN to a server inside the "best route ISP" network, because then your ISP _has_ to route your traffic through that peering exchange. I.e. the additional latency of doing the VPN stuff is still less than the additional latency of having a poor route.
Hops also aren't a particularly useful abstraction here. They don't align with latency very well; the only thing a hop implies is that a router has to get the packet and route it, but that's a huge variance in latency. A hop could take nanoseconds or it could take hundreds of milliseconds. The number of hops doesn't really imply anything useful about latency.
All that is to say that yes, I believe under some circumstances the VPN could give you lower latency (with a bunch of asterisks). One asterisk is that figuring out whether your peering is good or bad practically requires a network engineer to look at your routes, it's not an easy thing to figure out. A second is that those routes change frequently, so just because the VPN helps today does not mean that it will tomorrow or even for the next hour. A third is that these solutions are likely somewhat custom; each ISP or maybe even each network segment will have particular links that need to be avoided, which means each ISP/network segment will have particular IP ranges that "encourage" the correct routing. Figuring out which to use would be non-trivial.
In TLDR form, I think a network engineer willing to spend like 4 hours analyzing their network to set up a VPN that will shave 5-10ms off their latency to a particular game for a limited amount of time could probably do so. It's within the realm of possibility that some company is doing a Thousand Eyes-like thing and actually creating optimized VPNs with the same strategy. My suspicion, however, is that they just tell you to log in and try your latency on a bunch of servers til you find one that's lower (at the present moment) and then they hope you never check again.
Games have largely moved away from direct connections and user hosted servers though. The players and companies prefer the modern match making system. Its easier to use, more reliable, and gives the company greater control over the experience.
How much of that is because of (CG)NAT though? You can still do matchmaking and have direct connections. Yeah, there are trade-offs, but when you look at for example the fighting game crowd where latency is a big deal, consumers may massively prefer it.
(Either way, a "gamer" branded product that is unlikely to actually help in most real gaming scenarios is 95% of "gamer" branded products.)
Honestly, I'm genuinely surprised no ISP has started doing "gamer" marketing as it seems to be so effective elsewhere, "We give you real public IPs so you can connect directly to your opponents for lower latency, get on the internet fast lane!".