The best is to go for hardware wallets like Trezor which is open source, supporting many cryptocurrencies and yet store private keys offline.
Exact. I would never manage large sums of cryptocurrencies via a smartphone, if then only in readonly mode via Cointracking.info, for example. The chance that the smartphone will be stolen or someone will get access to the keys through malware is simply too great. In extreme cases, all it takes is the installation of a scam app and your hard-earned coins are gone.
Hardware wallets give you so much more security and are also compatible with a smartphone, for example the Ledger Nano X. Here is a youtube-video showing how you can pair your HW with your phone:
Ledger Nano X — Pairing your device