In this case, the N+1 is harder to justify because a capable steed that performs the same function (MTB) already exists in the OP's corral.
But the Redundancy and Selfless approaches are truly valid here, and improve the OP's quality of life, and are reason enough to get another MTB (of equal quality and materials to the existing one), with one bike being kept and ridden by the OP at each location.
But what wasn't justified at all was the carbon frame upgrade on the new redundant bike, as well as the other upgrade expenses that typically come with a carbon frame (hydro disc brakes, longer travel (and lighter) fork, tubeless rims/tires, higher quality front/rear suspension, etc...), all of which make the bike easier to control in sticky situations, and more likely to avoid a fall in the first place, and therefore make the justifications of the those upgrades covered under the "Safety Approach". Using these upgrades to avoid just one fall and the out-of-pocket expenses resulting from the ambulance ride and Emergency Room visit would easily pay for those upgrades.
Other purchase requisitions that are covered under the Safety Approach are: toasty warm winter shoes, dynamo hub, studded snow tires, fancy polarized glasses, light-weight MIPS helmet, etc...