This issue is at the heart of supporters at live football matches vs TV viewers. Sporting authorities are mostly there to maximise income for themselves and their business partners. It would be good to think that they have some underlying altruistic motives, but (professional) sport is about making money. As such, the income generated from a few tens of thousands of ticket-buying supporters pales into insignificance when compared to the money made from selling TV rights, around the world. This in turn means that the Premier League doesn't give a stuff about people actually going to watch a match in a stadium, since the income from such people is relatively paltry. I suspect that, given the chance, matches would start at any time, on any day, that would provide the highest level of TV-related income.
Having said all this, the TV companies are aware that matches without crowds do not have any atmosphere (as seen during the season when Covid rules prevented fans from going to games), so they don't (yet) take extreme liberties with fixture timings, in order to encourage (or at least, not discourage) people to actually attend.
The specific situation with the mid-week FA cup fixtures is a result of the Premier League generating vastly more income for clubs than the FA Cup could dream of. Consequently, any decisions about shuffling PL fixtures, or moving cup matches, will always be heavily weighted towards league games. We supporters are far less important to the money men than the TV audience, and football, at least higher echelon professional football, is now a business first, and a sport second. In summary, Saints are now so good that we don't get to choose when to play. It's all about money.
Right, I'll get off my high horse, return my soapbox, and go back to the Northam End, where I can sing (Zouma, Zouma, you're a c**t)