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If somehow I have an address with its corresponding private key but I have no wallet (well maybe I use some wallet to generate the address/key and then throw it), would it make sense to collect coins to that address and in the future redo the wallet with the addr/key to handle them?
Does that make sense? I am thinking of it as a security police to not have a wallet on a computer (neither connected to the net or not)
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Absolutely! Generate your public and private keys using a wallet, save your keys somewhere, you can even print them on a paper and put it in a save place. I think this is the higher level of security.
Additionally you can split your coins in 10 wallets and print them separately. That way if you need only 0.2 bitcoins you can take two keys and import them in your wallet. This gives you flexibility.
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This makes a whole lot of sense for security reasons as you reasoned already. If there is no computer having access to the wallets private key it can be stolen (via software).
This is called cold storage or wallet. The normal case is a hot wallet.
One thing you should pay attention to though is that you will be able to access your funds in the future. There is this question concerning future compatibility.
This is perfectly acceptable, however given human nature, it may be likely you lose them. If you lose those 256 bit numbers (however long they are) that's it you have lost your money. So DO NOT bother asking how to recover the private key. There is no way. Also you can generate the address (public key) from the private. So do not lose the private key. – marshal craft – 2017-08-25T10:44:06.307