As for Arteta, I suspect the board hope the new manager will be easier to control and modest in the transfer market.
A Mourinho type would have arrived with a 200 million pound shopping list and make frequent outbursts on TV about how the club needs to support him with transfers etc. There may be an assumption that Arteta is easier and cheaper to manage. Mourinho for instance wouldn’t have stood for the only January addition being yet another injured loan signing whereas they may feel Arteta can be told “this is what you’re getting.”
At the very least, he knows what it takes to play in midfield in the EPL. If he came as a player manager he’d instantly improve our central midfield even at his current fitness level. To be fair, he'd improve central defence tenfold too.