Unfortunately, the "aspirin" paper is behind a paywall. But based on the abstract ...

I don't get why a PwP would benefit more from increased tyrosine hydroxylase levels than from just increasing their levodopa dose.

Tyrosine hydroxylase (TH) is the rate-limiting factor in the conversion of tyrosine to levodopa. But, as I understand it, it is not directly involved in the conversion of levodopa into dopamine. [1, infered from figure]

......................TH.......................... .........AADC
tyrosine --------------------> levodopa ------------------> dopamine

So, as I understand it, increasing TH leads to an increase in endogenous levodopa.

But couldn't this benefit be more easily met by increasing the intake of exogenous levodopa?

Perhaps the marginal benefit of increasing TH over increasing exogenous levodopa comes from TH having a longer half-life. Perhaps, it also has better localization properties.

Reference:

[1] Tyrosine hydroxylase - Wikipedia

John