You can do that but if you only rebalance once per month (1 month is about 22 trading days), your entire annual performance is derived from only 12 prediction output files which is more risky than speculating on 52 predictions. Your Numerai signals staking performance is going to be based on 52 predictions but if you only speculate with real money on 1 out of 4 of these windows, you might have a very different real average performance, as you might miss out on some of the best or worse 4 week window predictions.
In general, the whole idea with algorithmic trading is that you want have as many trades as you can on as many predictions as possible over a given timeframe. Imagine having an uneven coin where you know you have a 51% edge of winning a coin flip, you are much better off doing 10,000 coin flip bets of USD 10 each than 100 coin flips at USD 100 each. The odds of being a winner after 10,000 coin flips is much great than with only 100 coin flips - even if the overall USD amount at risk is the same.
I’m not 100% sure but I would think that with a limited pool of money, a weekly prediction timeframe is probably more profitable over time if transaction fees are very low.