Do punctuality, reliability and fares affect patronage levels?
Much of this is down to what economists call elasticities of supply and elasticities of demand.
On the railway supply is very inelastic, and in the short term, it is often fixed, especially in the most congested parts of the network. Even if the infrastructure can take more trains, the supply of rolling stock and traincrew is difficult to increase. In particular supply is much more inelastic on the railway than bus services or airlines, because the way the railway operates makes it much more difficult to reallocate rolling stock and traincrew from one route to another.
Some demand is inelastic too, most notably travel to and from work. People choose where to work and where to live, and are then stuck with limited choice (and sometimes no choice) on how to travel between the two. Sometimes the only way to escape high costs, poor reliability and unpunctuality is to change jobs or move house. Now working from home can be a partial solution too, so travel to work is possibly more elastic now than it used to be.
On the other hand, most demand for leisure travel is very elastic: price matters, and bad experiences of reliability and punctuality put people off using the railway again.
Business travel is an interesting case. Before Covid demand would not have been very elastic on price but much more elastic on reliability and punctuality. That's probably still the case, but technology has shifted demand downwards.
The industry seems to put more emphasis on expanding capacity rather than improving punctuality and reliability.
Other things being equal, expanding capacity should improve punctuality and reliability, though I expect that some people won't see Thameslink as in that category.
And some new infrastructure is primarily for improve punctuality and reliability, the Hitchin flyover being a good example.