I think you have missed what the problems are... Even if a player is doing everything right on their end, enabling UPnP/portforwarding, etc, etc, the ISP can do some game breaking stuff, like carrier grade NAT, this is what your home router does, but on a much larger scale, and this one you cannot control. This was not very common in North America/Europe before, and pretty common over in Asia/Australia etc. but with more and more mobile internet connections, this is now creping up all over the world now. And this for the most parts makes direct connections between two users harder and harder to do...
And this is not covering all the other shenanigans ISP can do with traffic shaping and how they route their traffic etc, so some really strange things can be seen when you trace your traffic.
So when you enlist a VPN service, they give you a public IP with much less traffic filtering on what you do with that access. So even if your traffic has to go to via the VPN provider and then exit in the location you desire, this bypasses alot of things your ISP might have done, like Carrier Grade NAT. So yes, your ping could be worse, but things like P2P connections can work alot better, improving time it takes to instance with the other players for example.
Also, choosing your exit node is also very useful in with who you want to play, as many P2P games favours matchmaking with players in your region, so if you are an Aussie player who works strange hours, and can play Elite when Europeans play, choosing an exit node in Europe can have a huge impact on how well the instancing works with European players.
Here big VPN providers usually tend to choose locations to place their VPN servers on connections that have connectivity between the datacenters,
I have encountered an instance where two friends lost their DSL connections due to their operator said they would repair the telephone lines, that got destroyed in a huge storm, so they where not alone in losing this phone service, so instead of fixing the old telephone lines, the phone company put up new Mobile Phones Towers, and simply referred all their used to use their mobile service instead at mostly the same cost as their fixed services had before. Yay, this was back when crappy 3G mobile internet was all the rage, so not only is the internet connection over 3G really bad to begin with for gaming experience, they also got plagued with Carrier Grade NAT and other sneaky stuff, making their gaming experience almost none existent, so they had to sign up for VPN service, this would fix all but one issue, the crappy ping on 3G connection, so we had to suffer they had bad Ping, but atleast we could play together again.
The original issue was "congestion", or "decrease lag". Nothing about enabling connections at all, which is a different kettle of fish.
Using a VPN to circumvent the game provider's matchmaking limitations - nobody argued about that. Yes, it works (why shouldn't it) - which is why some game providers are filtering the use of a VPN.
Using a VPN to circumvent your ISP's (country's, employer's,...) traffic filtering works - until the point when using a VPN becomes illegal and/or VPN traffic is filtered. But still, this has nothing to do with easing congestion from increased player traffic. And even if it works - it just means that the VPN traffic is routed differently, not necessarily faster or slower.
Carrier grade NAT is pretty common nowadays, mainly for IPv4 adresses, and in itself isn't necessarily a problem. It only becomes a problem if the ISP (usually) who is using the NAT doesn't have enough adresses to go around and needs to switch adresses during an ongoing session. See the point about the better ISP. A VPN won't prevent carrier grade NAT, either - it'll just hide it inside the VPN so any server outside the VPN won't see this specific NAT. That is, unless the VPN runs out of adresses and has to invoke NAT itself...
Here big VPN providers usually tend to choose locations to place their VPN servers on connections that have connectivity between the datacenters
Like I said above, in this case they're taking the "V" out of the VPN and are moving their data over a physical Private Network. Otherwise, the VPN traffic would still (ultimately) share the same cables as all the other traffic, just adding some more overhead (i.e. all those VPN wrappers). All you can ultimately say is that, even in this case, the VPN traffic
might take a
different route than non-VPN traffic between the same endpoints. Whether that route would be faster or slower is a different matter / and one that maz change for every consecutive packet.
Now I'm intrigued - let me try something.
Ok, just one shot - don't want to make my workplace admins suspicious

Ok, that's an extremly inconclusive result (or rather, it shows that I'm doing it wrong - but I can't do it right, either, without messing with my workplace VPN which I
won't do).
I have here two machines running side by side: my private PC (on which I'm typing this) and my workplace PC (work-from-home due to 'rona). The private PC is wired, the work PC is on WLAN and running through a VPN.
tracert (to the same server, also in Germany) gets 12 hops on the wired private PC and 13 hops on the WLAN work PC. Looking closer, a) the work PC just has an additional hop at the start, so it's probably going through my downstairs AP. Apart from that, those adresses I can match up match perfectly between both machines (one uses IPv6, the other IPv4). The only conclusion I can draw from that is that my workplace VPN isn't wrapping everything (ok, that matches up - it only wraps traffic to our intranet).