Any other solution would face the same issue that chess faces now. For example let us say, we imbalance the sides a bit more so that white has a more definitive advantage. That just means that players will alternate winning and you’ll have to play a lot of games before anything definitive happens. In a technical sense there may not be draws, but if it just alternates 1-0, 0-1 and so on, is it better than 0.5-0.5 and so?
Shogi allows early momentum to snowball (since a captured piece is your piece). This means white has a much more definitive advantage in Shogi as white has the tempo, so I don’t think Shogi will fix anything, it will just cause see-saws. In fact I think fixing this chess issue, is far harder than it looks, and may require coordination to move all chess players to a new tactical game that magnifies differences in playing capability far more than chess which already magnifies it quite a bit.