Get a folding bike, like a Brompton, that folds down to shoulder bag size in seconds.
Your idea will have you a slave to the bike and its assembly and disassembly. Plus, even a frame with detached wheels is very inconvenient to carry around, the chain will get you dirty, eventually the derailleur or hanger will get bent, etc. To safely and conveniently carry a disassembled road bike, you need a carrying case , and that's hard to carry on the bike.