White was bought in as a CB and Tomiyasu was bought in as a fullback. If Tomiyasu wasn't injury prone, he'd be an established part of the squad even if he wasn't in the first 11.
If we cut our losses with Tomi, it'll be because he's injury prone more than anything else. Largely speaking the players Arteta bought to steady the ship were over 25 and on shorter deals. Meanwhile Tomiyasu's contract was long term and he wss signed at 22 - no way does Arteta sign a 22 year old as a someone to just steady the ship without recognising there's further potential there. Plus until his knee surgery, Arteta gave Tomiyasu minutes consistently even if he was just coming off the bench (plus a start against Liverpool). If you compare that to Tierney who was completely frozen out then I think it's fair to say that Arteta rates him as a player.
That isn't to say that White will lose his place - he's our best right back - but unless a really good offer comes in then Tomiyasu will likely be around for another season too. Tactically and technically he hits all the right boxes.