Silly departure and arrival times is certainly a problem if using WIZZ but FR and EZY are fine.
Not really.
EZY have about 15 flights leaving 0600-0730 (by their aircraft based there) which means being there 0400-0530. There’s a few Luton based Wizz flights in that time range, but EZY have by far the majority. There are TL trains all night, but if you are getting to the airport for that time there is simply no traffic, and a door to door lift / cab / car for anywhere within 15-20 miles along the MML will be very competitive with the train. And of course anywhere not on the MML the car will be far easier.
Conversely Wizz tend to have a whole series of arrivals from Eastern Europe from around 0630, which then head back that way from around 0745 to 0900, for which using the train to access the airport by train is somewhat easier.
At the other end of the day all the Luton based aircraft return in late evening, and again this is mostly EZY. I’ve lost count of the number of times I’ve bee;on that shuttle bus from the airport to the station around midnight.