> The problem for your case is that there are not enough train paths to add a new train,

I can find no indications that the lines in question are anywhere near capacity. Even if they were, adding new track to create such an arc around London would be far cheaper than continuing the crazy efforts add capacity in the centre.

> also your case would not produce a viable service as not many would use it.

This is entirely backwards thinking. It's how we've ended up in this mess in the first place. You need to guarantee commuter level service as a means to drive economic activity and demand for housing, then you can expect use. That requires a 20+ year commitment to get people to take the routes into consideration when moving or setting up a business.

This, much more so than the specific path, was the crux of my argument: It's stupid to induce further demand in the centre rather than investing in inducing demand in places where further expansion is far cheaper by reacting to congestion instead of planning ahead. Don't fix congestion where it occurs when it is expensive to do so. Instead route around it and make it attractive to avoid.

> The speed of the services also matter as the Clapham Junction to Guilford direct train is significantly than the Clapham Junction to Guildford via Epsom.

It sounds like you've misunderstood me. Clapham Junction to Guildford via Epsom is certainly not what I was arguing for. That'd entirely defeat the point of connecting towns outside or on the edges of London while bypassing the overloaded central routes and stations. If you're already on the South Western Mainline I fully agree it makes no sense to go off it before you can get directly onto the line to Guildford.

The point of what I suggested was to provide an example of avoiding a detour in towards the centre entirely in the first place. Hence the example of avoiding Clapham entirely when coming from Croydon, as one example of a way of improving connections between towns big enough to form viable commuter paths given time and opportunity to for people to take it into account when moving.

The key point of that example is that the travel time from West Croydon to Epsom + travel time from Epsom to Guildford is already competitive with the typical (but not the fastest) travel with interchange at Clapham Junction, but the trains run rarely enough on those routes that the change at Epsom will almost always make it significantly slower not due to the track or the stops, but due to the lack of frequent enough and direct trains.

A direct service would cut the average time via that route significantly enough to be competitive on time even without any track improvements even if still stopping at every stop. Even just that would be an improvement by removing the annoyance of a change.

> due both to track speed and number of stops.

As pointed out, on the line I actually talked about, track speed is sufficient, though not great. But gradually upgrading tracks on a relatively lightly loaded line is also a lot easier and cheaper than building new lines - the point was not to avoid the need for upgrades, but that it is possible to start a service without having to build entirely new lines.

> The extra milage here is cut by the speed of the longer part and the CJ-G runs on 4 track rail so allowing it to miss stations whilst the other lines have to stop everywhere.

There's no inherent need to stop everywhere even if fast trains and stopping services runs on the same tracks. Plenty of places run express trains and local trains on two tracks with careful timetabling. E.g. ensuring stopping services wait at stations if necessary. I grew up with that. Yes, it has challenges and causes delays at times, and yes it sometimes makes the stopping services even slower, but it works up until a service frequency well above the current one on the lines in question, at least for parts of the route. As a starting point for services you'e pointed out not many would use at the outset it's perfectly fine.

> Much better examples of hub-spoke issues are north of London between East and West Coast main lines.

Great, but that's entirely besides the point, which was not the specific route, but the overall idea of connecting towns on the edges of London together to reduce the need to go further in.