I am surprised that Ash reacts even slightly surprised, wasn't it hinted several times that both he and Maika already successfully assumed that Arthur hides their true self for political reasons? and it is not like there are so many nobles in the kingdom where this setup would make sense.
Maybe Ash has yet to understand the scale and gravity of noble political fuckery. He referred to Lord Itsuki's bloodline as "distinguished", despite him being a "mere" lord regent. I dont think it's been mentioned yet what the actual lord's noble rank is, but in other isekai works the chief of staff position is like being the head Knight.
Also interesting how ladies-in-waiting also serve as bureaucrats, implying this kingdom may have a relatively simple/horizontal power structure. Iirc this kind of thing didnt happen IRL until after our nobles lost a shit ton of people to the Black Death and severely needed servants, regardless of their bloodline. With such a flat power structure, a wealthy merchant's succession issues start looking quite similar to a royal's. TLDR too many possible non-royal answers regarding Alicia's circumstances to have Ash directly conclude she's a royal princess.
A novel reader may be able to shed more light into this peninsula's political structure.