Is it possible and make sense to integrate anti-keylogger directly into monero wallet, so keyloggers can't read and steal seed/password?
No. A keylogger can run on your keyboard's firmware, or in your computer's BIOS, or as a rootkit. In fact, a sophisticated attacker doesn't even need to drop a keylogger on your computer, they just need a device that is within range of your wifi network and they can detect your keypresses based on how they interfere with the wifi signal.
The answer is not to try defeat keyloggers, it's to use some form of 2FA, which in cryptocurrencies normally comes in the form of a hardware wallet such as Trezor, Ledger, or Keepkey.
It would be possible to include binaries for a anti-keylogger or anti-malware program
This would be a huge waster of time for Monero developers. Monero is a crypto-currency not a anti-malware company. There is no shortage of other sources for anti-malware software that are of high quality and likely to updated more often that what Monero developers could provide.
Two factor hardware devices such as Trezor, Keepkey, and Ledger have keylogger countermeasures. Experimental Trezor software exist for the simplewallet.