I get that the phone can't check for new messages all the time because battery and stuff but wouldn't it be possible to have timestamps for first/last message i

I get that the phone can't check for new messages all the time because battery and stuff but wouldn't it be possible to have timestamps for first/last message in a converstation or something so the phone could detect that if the conversation was going on for some time already on different device then it shouldn't notify about it? I mean it doesn't sound like rocket science, are there any deep architecture problems with that ?