The most reputable ones are probably: Exodus, Jaxx, Coinomi, Eidoo, Enjin (some of them had security issues in the past). The downside of these wallets is that they are not open source so you will have to take the developers word when they say "We're not sending the private keys to our servers". I wouldn't suggest using these wallets unless you are using them for holding small amounts. I recommend buying a hardware wallet, both Trezor and Ledger support BTC, Ethereum and all ERC20 tokens, in addition to some alts.
In order words, would it be safe to say that no wallet is 100% safe, apart from the hardware wallet? Since the hardware wallets are equally multiple coin wallets, what are their downsides?
Hardware wallet are also not 100% safe. your house could burn down and you'll lose your funds aswell.
Some downsides of a trezor/ledger are:
You cannot store any coin on them, they only support a specific amount of coins.
They could be expensive, not everyone can afford to spend another 100 bucks on basically a USB.
For them to work you'll always need to physically carry them with you. (Unless you import the seed of the ledger wallet, but then what's the point of the ledger in the first place?)