Can't sump basin be shut so it can't overflow?
You'd stop the flow for a while, then it would come up through all the joints and cracks and gaps in the system. (A home's foundation and floor are not really like a swimming pool. They're not intended to be water-tight. Very little pressure would be present.)

What you'd be left with is essentially a home without a drainage system, subject to all the flooding and related unpleasantness of centuries past.