Disadvantage is tubeless can be a fiddle to set up and it doesn't always work.
OP, You may well benefit from tubeless tyres, because once setup right, they require minimal fuss. HOWEVER the above stands true. I want to stress I got a good 8 months trouble free commuting, doing 100 miles a week on a pair of tubeless tyres. Look at the kind of abuse they can withstand here:
View: https://www.youtube.com/watch?v=G2OqwuhNGfg
The major downside is the sealant needs to be topped up and replaced relatively often, every 4-6 months as a bare minimum I think. It can be injected with a special kit by removing presta valve cores, or simply poured into a partially seated tyre. I don't have the kit and valve core removers, so I do it the simple way. You could out source the task given your aversion to fiddly stuff.
However, if you have problems setting up tubeless tyres, they can be a real headache, sometimes taking a few attempts to get a good seal. Funnily enough, my first installation went very smoothly, I was up and running after the first attempt, all with virgin components. I was very enthusiastic about recommending them to every Tom, Dick and Harry I met. THEN came the second attempt. After 8 months, along came the day I got a slow puncture, the tyre was out of sealant, having dried up, or otherwise used up doing its job sealing punctures as I went. Resealing the tyre that was used and dirty was not so simple! After 3 failed attempts to form the seal on the rear tyre I have reverted to using a tube in my rear wheel until I can find the time to work on the wheel again. I have a new born baby at home (I didn't when I first invested in the wheelset) so I have less time to work on bike niggles. Hence temporarily giving up and reverting to tubes. I need the bike to get to work, so it was an annoyance to get to the bike with a flat in the morning 3 days in a row. For someone with more time on their hands, it probably wouldn't be a big deal!
If you have the option, a handy friend, son, brother or friendly neighbourhood spider... er, bicycle mechanic can deal with the finger/head-achy parts and you can just focus on the riding. Being perfectly capable mechanic myself, I cannot justify out sourcing the work, I just need to find the time. So despite my own experience, I would recommend tubeless tyres to someone who can afford to get a mechanic to deal with the work, or has lackeys on hand to do the work, and you can focus on the ride.