In grassroots matches with one referee, in tournaments, or when there is a queue of matches… with flying subs… it makes sense to let the teams choose their takers from the whole team. It’s simpler, faster, better.
With flying subs the ref does not have a record of the 11 on the field. At full time in grassroots with flying subs, especially in tournament football with other teams hanging around, tiny pitches, especially with kids, especially in cultures that like a huddle… it is unrealistic for the referee to know who the 22 who finished the match were - or to police this. Please understand this.
This is not the typical set of circumstances in the UK so your milage may vary. In other countries, culture and competition rules may vary. I have refereed KFTPM at grassroots with flying subs a lot. When our comp rules were to only select from the 22 on the field I could not enforce this. I had to trust the coaches (and I would mention it in pre-match). Now that the coaches just send the next player it is much quicker and more inclusive. I am still looking down at the list of numbers as it grows with takers to avoid duplicates - just as with any other big match shoot out!