Finnish doesn't have umlauts. Characters ä and ö are entirely different and separate from a and o so it doesn't make sense to add the letter e signifying a-umlaut or o-umlaut when writing in Finnish. German has umlauts so it makes sense to write either ä or ae when writing in German.

I agree it's best to write Maatta if letter ä is not available. I suppose the vocal harmony makes it easy to distinguish whether a is supposed to be a or ä and if o is supposed to be o or ö.