Luton has genuinely good public transport for an airport of its size. The Luton DART shuttle link to Luton Airport Parkway station takes under four minutes and runs 24 hours a day, and Thameslink trains reach St Pancras in around 30–40 minutes including that connection. For a single traveller with one bag and no time pressure, that's a reasonable option. It's worth being honest about where it starts to make less sense.
Luggage: Standard commuter trains have limited dedicated luggage space. That's rarely a problem with one carry-on; it's a real one with two large suitcases, golf clubs, or a family's worth of bags, especially if the platform-to-DART changeover happens at pace.
Number of travellers: Rail and DART fares are charged per person. Once you're travelling as two, three or four, a fixed-price private transfer for the whole group often works out close to or cheaper than everyone's individual train tickets, and you're not each carrying your own bags through two changes of transport.
Time of day: Coaches and some rail services thin out late at night and in the very early hours, which is precisely when a lot of Luton's low-cost flights arrive and depart. A pre-booked transfer runs on your schedule, not the timetable's.
Predictability: A taxi or private hire app booked on the spot at Luton is subject to surge pricing at busy times, and you won't always get the same driver quality or vehicle standard twice. A pre-booked fixed-price transfer removes both variables. The price and the standard of service are agreed before you travel.
Door-to-door versus multi-stage: Trains and DART both get you to the terminal, but rarely to your actual front door or hotel entrance. A private transfer is one vehicle, one journey, no changeover.
None of this makes the train the wrong choice. For a solo traveller on a fixed budget with light luggage, it's a perfectly good option. It just isn't the right choice for everyone, and a private transfer earns its price back most clearly for families, groups, business travellers, and anyone flying at an hour when public transport options thin out.