You mean to send btc from each different wallet to the new wallet then withdraw it all? I think that's a good idea in my own opinion. Correct me if i'm wrong, if I decide to cash out my btc it would cost me lots of money for each transaction fee when it's in different wallet and not in one wallet. I just check the thread made by loyce it seems if cashing btc you'll need enough btc for deduction of btc when withdrawing with high fees.
Every transaction you receive is counted as one input, and every input you spend increases the weight (or size) of the transaction along with the transaction fee. If you're getting paid multiple small inputs for signature campaigns, etc., it's a good idea to send/consolidate all of them into one or two addresses while fees are low.
But yeah, spending from different wallets would be more costly. It's more expensive in fees to spend one input each from two wallets (basically two separate transactions) than two inputs from a single wallet (one transaction).