I don't think they would fit so well for bitcoin, as btc don't have all those smartcontracts and dapps yet.
Be careful as new is not that safe.
It's a web wallet which you expose your keys all the time..
Metamask and MEW are so popular not because of smartcontracts and dapps, but because it's insanely hard to use any sort of desktop wallets for Ethereum - the blockchain is bloated and even pruned mode doesn't help much, because the syncing is painfully slow and consumes a ton of RAM and CPU time. So, ETH users don't really have much of a choice and have to use this type of clients.
I'm sure there's plenty of Bitcoin wallets in a form of browser extensions or html pages, but people don't use them because there are much better options like good old Bitcoin Core or very popular Electrum.
Its more of security issues that most are probably not using those webwallets. Hacking and phishing is very common. Lots of users were using blockchain.info wallets before, I don't know why this site seem to be trusted but I guess it works for them. Registered users has their mnemonic phrase and private key which I guess made them trust it and they can sign a message too.