Does this thermostat/furnace wiring make sense?
Many thermostats can figure it out on their own these days

Modern "smart" thermostats such as Nests and ecobees have electronics inside them that figures out if they're being powered from Rh, Rc, or both, and handles the situation accordingly (usually giving preference to Rc if power is present both places), which means that they don't need a Rh-Rc jumper.

If your new 'stat does need the jumper, it will come with it

If your new thermostat isn't that smart (i.e. needs a Rh/Rc jumper), it will come with one, similar to the one on your current thermostat.  This jumper is needed because the thermostat doesn't have the electronics to figure out which terminal to draw power from on its own, and some situations (such as boilers, wall furnaces, and the likes) require the thermostat to keep the heating side power (Rh/W) rigorously separated from the cooling side power (Rc/G/Y).