That's an interesting idea! That ending really does look boring but anyone who plays the Budapest will probably suffer more than you, especially if you're prepared for it.
Here are some links on that position.
https://www.chess.com/explorer?moveList=d4+Nf6+c4+e5+dxe5+Ng4+e6&ply=7
https://www.chess.com/games/search?fen=rnbqkb1r/pppp1ppp/4P3/8/2P3n1/8/PP2PPPP/RNBQKBNR%20b%20KQkq&sort=3
I do not study chess openings too much, and when I do, I am not studying the Budapest Defense. Very recently, I had a try with 4. e6 as white instead of moves like Nf3 or Bf4 which I think are the main moves for white. I have always played the main moves against the Budapest Defense but I feel that 4. e6 is good too. I can not find too much of a weakness with 4. e6 as the way I play against the Budapest Defense, I most times lose the e5 pawn anyways, and in my opinion, 4. e6 is good because is black takes with the d-pawn, then there will be a queen exchange and black can't castle. However, black seems fine and it will be a slightly dull endgame (in my opinion). However, to avoid the exchange of queens, black will sometimes take with the f-pawn and I think this move makes the king weaker.
So my question is is 4. e6 good even though it is not one of the main moves (correct me if it is one of the main moves, I don't know enough about openings) and if 4. e6 is not good, can someone tell me why it is bad or why the main line is better?
Thanks, Ral.