More that 'PL proven' seems just as hit and miss as non PL players. With the added risk of inevitably that player being on a) a higher salary (and so you will need to pay them more) and b) commanding a higher transfer fee I don't think it's really a thing at all. More that people, like us fans, have more comfort around players we know and see regularly and feel we 'know' when in reality we really don't and don't have a great sense for how they'd do in another setup.
Re Arsenal, if I think about their key players: Saliba, Gabriel, Rice, Partey, Odegaard, Saka are probably who I would think are currently nailed on starters, maybe you can add White now although Timber will displace him I feel long term, for argument's sake given he had a big fee you can add Havertz as well. It's pretty even between PL and non PL and I'd say their truly elite players are Saliba, Rice, Odegaard and Saka. They definitely have been bargain hunting around the PL with limited success though, lots of cheaper and free deals like Jorginho, Willian etc.