The number is used not because other pilots are supposed to actually be able to look out their window and see your number (if you're that close, you'd better be flying in formation on purpose!), but because it's a standard way of UNIQUELY identifying your aircraft. No one else has that number, so each unique number you here unequivocally means another aircraft in the area who has hopefully given a clear position/intention report. Really, there isn't another way to ENSURE that you don't inadvertently ascribe a radio call to the wrong aircraft. As many
Similarly, I'd rather hear "Skyhawk" or "Citation" than "Cessna"... I always say "Cherokee" rather than "Piper." Only one syllable off either way, and way more information. A "Cessna 172" is a Skyhawk.. use that, and reserve the numbers for your tail number in your call to avoid confusion. Your CFI will go over all of this with you. If you're trying to get a jump on starting training, download this handbook and anything else you find interesting on the FAA site...
https://www.faa.gov/regulations_policies/handbooks_manuals/aviation/airplane_handbook/