Of course it’s not impossible! And in fact you’ve just described my relationship to my own best friend. You have my deepest condolences on your loss. I don’t even want to imagine how that would feel.
Being able to have a bond like that with another person is a blessing and a privilege—and furthermore I don’t want anyone to mistake anything I say for privileging romantic love over platonic love, because one can be just as powerful, deep and abiding as the other. If Sherlock and John are passionately loyal platonic friends, it would not dilute in the smallest degree the profundity of their relationship. (Although it might be a checkmark in the ‘Sherlock as aromantic/asexual’ column.)
But of course you’re presenting a straw-man argument. I by no means believe that EVERY close relationship we see on-screen is queer rather than platonic.
Going by the ‘text’ of the show, however, I would say that we are being implicitly told that this one is.