It can of course. However, for as long as anyone can remember senate rule changes required 2/3 vote. As soon as that changes, the senate as we know it ceases to exist. It simply becomes another majoritarian body like the house.
I’m not sure that would be entirely a bad thing. The Constitution certainly has nothing in it about requiring super-majorities in the Senate for anything other than enumerated issues. I think the actual constitutional provisions for slowing things down in the Senate, such as the gradual replacement of members, is sufficient check on the House.