The Thameslink route is an outlier amongst British routes for having an overnight service. Most other routes don't have any trains later than about 11pm or midnight, or before 5/6am.
In most cases, that's just how it's always been; when BR was privatised, the Rules of the Route (RoTR - this became section 4 of the Engineering Access Statement) dictated that most lines without overnight freight/sleepers etc. would shut to traffic during the small hours, to allow ad-hoc engineering works to take place without trains needing to be cancelled or diverted. Changing section 4 timings is now a virtually impossible task - I've been party to extensive discussions for changes of just a couple of minutes either way...
The frequency of overnight Thameslink services was reduced back in December, as part of hamfisted efforts by the Department for Transport (DfT) to cut costs in the rail industry. Meanwhile, Elizabeth line services have never ran overnight, and other than perhaps on Friday and Saturday nights (where the 'core' might become part of the Night Tube in the future, as per certain sections of the Overground) likely never will.
The issue with Sunday mornings is even more pronounced, as this is traditionally when demand was lowest and so most overnight engineering work is done then; section 4 timings generally reflect this.
At the end of the day it comes down to the fact that, whilst having overnight services would certainly be possible, demand is usually low and so services would require a higher than usual level of subsidy. With the industry under pressure to cut costs (seemingly more so than increasing revenues) you are more likely to see overnight services withdrawn than extended.
