I honestly wouldnt have imagined that 3rd is the traditional "highest pressure", but I guess it makes sense.
Obviously it's all situational based on each round result but I'd have never expected that to be the pressure cooker.
Historically the best penalty taker went first... "getting off to a good start" was always seen as the best idea and having best taker there as a result... but a lot of coaches started to realise that the first penalty is kind of the least pressure (and actually it is the one most likely to go in even when adjust for quality of shooter, like ~5% more chance, guess some being pressure, some being goalies not kind of in rhythm etc) and also that so often shoot-outs were decided by the later penalties.
Soooo then a lot of coaches had the best taker 5th as the shootout going to 9-10 penalties is most "common" outcome and therefore the last guy has most chance to win it. BUT as stats have become even more prevalent? Well, 20% of shoot-outs never make it to the 5th penalty so putting your best guy there is kind of dumb and reduces odds of winning.
So then quite a lot of teams put their best taker 3rd or 4th.
Lampard started career going 1st then often went 3rd later in career.
Ramos went 3rd or 4th for Real.
Saka goes 3rd for Arsenal.
Ronaldo when at United usually went 3rd or 4th.
Aguero always went 3rd or 4th.
But it depends. Lewandowski always liked going 1st. Messi too.
Guardiola favours the old-school best taker goes 1st too... he has always put his best guy 1st... aside from Aguero who always seemed to want to go later.
Probably the most statistically sensible spot for your best taker depends on if go 1st or 2nd.
1st? Probably 4th in the order.
2nd? Probably 3rd in the order.
Just to ensure they dont get stranded.
But ofc some players have a preference too and so long as they dont go 5th coaches should probably just let them go where they want.