Can BTC switch to PoS in the future and remaining safe at the same time?
No, bitcoin would never switch to proof of stake, that would be 100 steps backward for the network, proof of stake consensus algorithm also promotes centralization, we can agree that it is not the best for a decentralized network.
Bitcoin functions just fine the way it is now, and some of the things you read about it in the mainstream media is just propaganda published to discourage people from using and supporting bitcoin.
Every algorithm sooner or later tends to centralization.
The problem is that every protocol promotes competition instead of collaboration.
In proof of work the advantage is on the side of the entity(ies) that invest more energy
and efficiency in the process of mining therefore the ones who have more money
to invest in hardware have more chance to win the lottery.
In prof of stake the advantage is on the side of the entity(ies) that have more coins
and locks more coins into the process of staking therefore the ones who have more money
to buy the coins have more chance to win the lottery.
In both cases there is a limit to participation by the flawed design.
To be more sustainable and democratic the algorithm should allow everyone to participate without limit
and not favoring persons or entities with more money, otherwise is not better that the current fiat (financial) system.
I hope that sooner or later someone will find a better algorithm and protocol that will achieve this
but until then we have to live with what we have.