I suspect it was designed with the gate on the right so you could use your right hand to load. Most people have more coordination with their right hand.
With Winchester centerfire lever actions, you can't top them off anyway. When loading, you insert cartridges until the rim is just shy of clearing the gate. You push it all the way in with the next cartridge, again stopping when that rim is just short of entering. Repeat until full. There is no cartridge stop like on a pump shotgun, so when a cartridge is fully inserted it's pushed back into the action by the magazine tube spring where it blocks the gate and prevents loading additional cartridges until the last round is in the chamber.