What exactly is the benefit of buying a hardware wallet for Bitcoin?
Hardware wallets are generally designed to securely store your private keys in an always-offline environment (&quot;cold storage&quot;). This allows the user to have confidence that their coins will not be stolen by malware/hacking/etc, since any attacker would need to have physical access to the device itself.
If nothing else, this is the main advantage of a hardware wallet: the user can securely store their funds, without needing too much technical knowledge or skill.

It's not like I can actually use it in physical stores.

Well, if the store accepts BTC payments then you could, but I agree this is a perhaps less important/rare use case at the moment.

And if I'm supposed to use it as a secure storage device for all my coins, doesn't it just scream &quot;STEAL/SEIZE ME!&quot; to burglars and the cops?

Yes, any educated thief/cop/etc may view a hardware wallet as a target for theft. Most hardware wallets have security against this though, such as a PIN to unlock the device (usually with the threat of wiping the device after some number of failed attempts). Each device will have different features in this way, so as a user you'd have to decide what fits your needs best.
Keep in mind that you can also just use the device to generate a wallet in an offline/secure environment, then create and test backups of that wallet, and finally destroy the hardware wallet device itself. In this way, you could create a cold storage setup, without the added risk of having a device which is obviously a bitcoin hardware wallet in your possession (of course you'll need to keep the backup, but the idea is that the backup may be easier to hide- for example using steganographic techniques).

why buy such a hardware wallet instead of just an encrypted USB stick with a wallet.dat on it?

If the wallet.dat file was generated on a computer which connects to the internet at any point in time (past/present/future), then you will not have the strongest of guarantees that it is not infected with malware. The same goes for the USB stick.
A hardware wallet, on the other hand, should be designed to have extremely restricted communication channels with the outside world, such that the user can have a higher assurance that their privkeys have not been leaked. In many cases, I've seen hardware wallets include a physical confirmation that the firmware running on the device is genuine.
Worth mentioning as well: no electronic device should be used as the only form of long-term storage for a user's funds. Bit-rot and general electronic failure are guarantees, given a long enough timeline. It is very important to have a physical backup of the privkeys as well (think: written on paper, stamped into metal, etc. This backup usually comes in the form of a mnemonic seed phrase these days).

Of course, if you're a technically savvy, then you may prefer to create your own cold storage device, perhaps something as simple as a raspberry pi running Tails as the operating system. But for many users, a hardware wallet offers a great mix of security and convenience, for a reasonable price.
The extremely adversarially-minded user may also feel alarmed at the prospect of a supply-chain attack against a hardware wallet manufacturer. They would be great targets after all! To combat this, the user may choose to use a multi-sig setup, with signing keys generated on multiple devices from different manufacturers, and perhaps even keys from bitcoin-core, etc, as well.

Ultimately, there is no 'perfect solution' for security of your funds, each user will have to make a choice based on their needs, preferences, and comfort level.