It's not a secret that people tend to overdo it when advertising and talking about their products and services on social media. Unstoppable Wallet did just that yesterday, trying to make it seem that it's better to use a hot wallet, like Unstoppable, instead of a hardware wallet.
This is the tweet I am referring to:

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They say that battery failures happen from time to time. OK. No arguments there.
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Carrying a hardware wallet with you is a signal that you own (a lot of) bitcoin and crypto. I would agree with that, and I have never been a fan of flashing your hardware wallets publicly. You never know who is around and could see it. I prefer keeping mine at home, safely tucked away somewhere.
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They go on saying that hardware wallet users become victims of phishing attacks. This isn't excusive to hardware wallets. The same schemes exist for software wallets, exchanges, and anything else crypto or non-crypto-related that scammers deem worthy of stealing.
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The native apps of these devices introduce various types of attack vectors. They introduce some and then they get fixed. The same can be said about software wallets. It's always a fight between good and evil.
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Hardware wallets aren't private and the vendors know your name and can see your balances. True, but it also depends how you buy them and where. Some companies sell their devices in physical stores, like Best Buy and MediaMarkt. Parts for DIY HWs can be purchased from various unrelated sellers online.
In the end, Unstoppable and other software wallets aren't better and safer than good hardware wallets.