If you mean Layer 2 is DeFi (a fake decentralized finance that's actually centralized) where you can easily connect your wallet to other sites without need to login or transfer your coins, it's not possible and Bitcoin don't need it at all.
It is possible, though like most things that are new developments, they should be used with caution and due diligence...but that does not mean it does not exist or is not possible. That's entirely a false statement. I think you should reconsider posting in the fashion that you have...making such bold and certain opinions when they aren't true can be considered as misinformation. As of right now, factually speaking, your post would be considered as misinformation to many (no offense intended).
Also, to claim that the entirety of Layer 2 DeFi on EVMs are "fake decentralized" is a very bold statement. I can understand your sentiment, but it is not appropriate to call the entirety of a large ecosystem that does include legitimately decentralized applications (through smart contracts) "fake". A lot of legitimate people are and have put hard work into creating new use-cases in the Ethereum ecosystem, and some have done a great job doing so. Uniswap, aave, just to name a few, are great protocols. There are many more out there though I won't go into naming names for the sake of validating this fact (I don't need to, it should be obvious to anyone who is actually keeping a close eye on all technologies).
To address the OP and defy the opinion that layer 2/defi/browser-based wallets etc. aren't possible...
Bitmask is an interesting project that has all of the claims of a private, decentralized extension where users have full sovereignty. It highlights that
it is indeed possible to have a metamask-like wallet to interact with the ethereum-like ecosystem that has been forming in the Bitcoin ecosystem for the last few years. It also open source, which is an important prerequisite before posting about it.
In my opinion, Ethereum will be superseded by the Bitcoin DeFi, NFT, etc. ecosystem, as the same functionalities previously exclusive to Ethereum/EVM networks start to work just as well for Bitcoin. It's not just possible on Bitcoin, this transition seems to be happening. More below...
Do you think bitcoin layer2 will come ?
Yes, many projects are paving the way behind the curtains. So-much-so that it seems even veteran of this forum aren't aware of the integration of decentralized finance into the Bitcoin ecosystem.
Think of EVM/Ethereum as the sandbox, and the integrations that are being developed in Bitcoin as the iterations of what worked in this sandbox, built with compatibility for Bitcoin.
It's definitely not finished, but it is
definitely happening. Look at CORE, orange, even icp have come up with some cool and
truly decentralized solutions. There are probably a lot more now though I was witnessing this all starting over the last year, pausing over the last few months, there are probably many more legitimate names than I've named out there by now.
OP (or anyone else for that matter) if you have any names that you want an insight on, I'm happy to have new names sent to my DMs so I can look into them. You help me by sharing new names, I help you by delving in with my expertise of what's actually using decentralized & open-source technology, and what's just using those buzz words (I'll never give financial advice, but just see things for what they are for you).
To anyone who gets told something is not possible, laugh at them! Nothing is impossible. Heck, take any of what Bitcoin can do and mention it in 2007, and what would the response be?
"That's not possible!" and yet...here we are.