As Japanese houses commonly have higher floor, the verb 上がる (go up) is appropriate, I think.
How about non-Japanese houses in which the floor has the same level? Is the phrase うちに上がる still compatible?
One more question, is it ok to use うちに入る instead of うちに上がる ?
I would still use 「[上]{あ}がる」 even if I moved to a basement or tepee tomorrow. I cannot speak for other Japanese-speakers but I myself do not really think of "going up" when I say 「[家]{いえ}に上がる」 even though the floor of my home is over 40 centimeters (two steps!) higher than the "genkan" = "entrance".
If I used 「家に[入]{はい}る」, I would feel as if I were a thief entering a house without removing my shoes. As a resident or guest, I would always use 「上がる」.
I might also add that even in the latest wheelchair-accessible condominiums with no elevated floor, people still use 「上がる」.
But who knows? A couple of generations after moving into a tepee, my descendants might be saying 「家に入る」 or the equivalent of that in Navajo.