why look for a single wallet , i thought your missing the old times ? so you can also do that again but if your old computer is working fine and can still support new updates from the wallet then theres no need to use a new computer .
what i cant only understand is your title , why say so when we all need a personal wallet to store our cryptos ? and if not personal wallet , what wallet should we use ? the one that is been shared ? thats risky .
The OP is noticing it a raise in a tendency that I have also noticed, it seems many newbies these days are not using their own personal wallets and instead are using the wallets given to them by exchanges, and while it is inevitable to use those wallets if you are a trader at the same time it is a mistake to leave your coins for long there.
After all it is not rare for exchanges to change their policies and suddenly you find yourself unable to get your coins out of the exchange, and we also need to consider the risk you are incurring by having your coins there when we know that hackers are always trying to gain access to exchanges and many times in the past they have been successful and have stole fortunes from them.