Beyond waves wallet I do not agree that desktops are safe
You find it difficult to synchronize it
You find it hard to back up the keys to the platform wallet too
If you have a slow internet connection, yes, you are right, it is difficult to synchronize. I use Electrum wallet, that has been ported to many cryptocurrencies. The good think of Elecgtrum, is, that it has it's own network of servers, that keep the blockchain, so no sync is needed. These kinds of wallets, are called light wallets, because they don't keep the blockchain. You may find a light wallet, that you control the private keys, but you don't have to keep the blockchain. With a light wallet, there is no blockchain sync phase.