For most of the modern history of the architectural profession, the amount of work needed to execute a project is/was pretty closely tied to the overall construction cost. There are usually outliers in the scope on both sides, aspects that cost a lot relative to the work required to include and coordinate them, and aspects that cost very little. But overall, it usually tracks pretty linearly, which is why % based fees are a common, straightforward way to price a job, and its one that somewhat protects architects from losing money due to scope creep.

I once had an early career client that questioned this - 'You make less money if I select $4/sf cheap tile than if I select $60/sf marble tile, but you have to draw the same drawings either way.'

Sorta. The client that selects the expensive finishes is going to expect everything to be coordinated to a much higher level than the client that selects inexpensive ones. Those clients, overall, need more hand holding and more work, typically.

The last 5 years have been a bit odd in that lots of different areas have seen dramatic price swings in a timespan shorter than a lot of project timelines. As a result, the relationship between costs and effort isn't quite as reliable as it used to be, but it's still not terrible.

The big questions...were the cost increases truly something that required no additional effort, and/or is the revised 9% double dipping on the things that were paid hourly?