The requireMenus start on day one, regardless of producing any income. What follows related to the US tax code in general, the us/Finland tax treaty might make exceptions about some of them:

You will be unable to hold any financial asset other than cash or deposit (no broker will let you do stocks for example - or an ETF)

You will have to report and pay taxes on the fantasy gains on your locally accumulating pension funds, even though you will not have access to them until retirement (if then).

You will have to file your company paperwork locally, but also as if it was American - with requirements that become more onerous with your ownership percentage (starting at 10% or 25%, can’t remember - luckily for me in that respect, I was below the reporting threshold most years - but I did have to translate and file financials at some point)

I had done all of these for many years. If you don’t enjoy the bureaucracy, you might be better off NOT owning a non-US company.

Why would you want to start a Finnish company? For targeting purely Finnish clientele?

From the guide it sounded like you need a Finnish limited liability company to be able to service domestic Finnish clients.

Or would Finnish companies be able to pay an on-site freelancer with an American LLC just as easily?

I don't see why not. In fact, it would be "cheaper" for them because they do not need to pay the value added tax to your non-EU company. Sure they'd get that eventually back from the tax office if they were paying just another Finnish company, but it would still take a bit of time.

I think Finnish clients can work with an American LLC. I'm not 100% sure, but I can't seem to even imagine why not.