I ride bitless and I compete.
Now just to qualify - they ARE competition legal...just not DRESSAGE legal. You can SJ and XC bitless all you like...(although some places will rule it must be a bitless bridle and not a halter, like many insurance companies, and you can't compete in 'SJ Style' classes that some RC's hold etc...)
I compete SJ and XC bitless - I went to the UK Chasers national finals last year bitless in our dr cooks. You can def use the bridle BE for the sj and xc phases - you'd need to check with BSJA but I'm pretty sure legal for that too.
BD and dressage under BD rules is where they aren't allowed. (including the dressage phase of BE) - and then showing.
For this, I use a snaffle. I ride bitless at home, but not all the time. My horse works better bitless and so I do do some flat schooling sessions bitless as it improves his way of going, encourages him 'up' in self carriage beautifully, and he is incredibly light on the forehand with it. However I'd be asking for trouble if I then all of a sudden slapped a bit in his mouth on the day of a dressage show

. I try to balance our riding 50/50 bitless and bitted - our flat schooling maybe 60/40 in favour of bit, purely because he needs to know and accept my aids in the snaffle too.
Whilst your aids are usually the same bitted or bitless, the pressure is applied in different area's for the horse (mouth v nose primarily - and depending on which bit or bitless you use, other areas too). So your horse needs to be accustomed and settled in the bit before they are likely to be fully settled and working well in it.
I would suggest that if you plan to dressage (or show of course), that you work the horse bitted, whether that is bitted only or bitless aswell. You'd be unlikely to be able to break your horse in a bitless and only ever use bitless at home, and then get a positive response from a bit at a show. If you want to compete in bitted competitions, but also be bitless - use both, but use both at home
It's up to you whether you start off bitted or bitless at the early stages or mix between. But there's no reason your horse won't learn both methods and be comfortable with both methods at home and hence also at a competition, keeping all your options open to compete in any and all spheres when he's old enough
Good luck x