Not a pilot, but yes they do take extra fuel. I believe it's like 5% of the trip total as extra for taxiing and weather reroutes, plus enough to get to an alternate airport if your destination is not viable. Plus aircraft carry an emergency reserve of 30 minutes worth of flight time. If you break into that last bit, you're likely declaring an emergency and ATC will give you priority sequencing to land.

You want to have enough for safety and wiggle room, but not just full to the brim as that's a lot of extra weight to carry around, which means you burn through fuel faster.

But even if airlines were to transition over just their short haul flights, that would make a huge difference in terms of fuel/emission savings. It doesn't have to be all or nothing.

When I worked in ATC I learned that airlines (here in Canada, at least) drafted up 3 flight plan proposals for each flight. One was the shortest time, one was the most fuel efficient routing, and one was the cheapest (considering fuel and ATC charges for how many sectors you cross, etc).

I'm sure it wouldn't be hard to factor in alternative fuels when making those calculations.

To add to my previous comment, taking the 787 Dreamliner that someone else had mentioned, you're talking a max capacity of 223,000 lb, and maybe 10,000 lb an hour. Flying JFK to LAX is a joke with that capacity. Definitely room for a less dense fuel in those tanks.

You're assuming that aircraft are already filled up to max, and thus would need extra tanks and being reinforced to hold them, etc.

That's just a wrong assumption though.

Take most any flight within Europe, or even coast to coast US like JFK to LAX as u/slowslownotbad mentioned. These flights run a couple hours, 5 tops, right?

Now let's look at an aircraft like the 737-800. It burns ~5,000 lb of fuel per hour, with a max capacity of 46,000+ lb. A 5hr flight would burn 25,000 lb of fuel. You take enough fuel onboard to get to the destination, plus an extra amount in reserve (startup, taxiing, weather diversions, holding pattern at destination), and then enough beyond that to get to an alternate airport if you can't make the planned destination.

For the sake of argument, let's say that added up to 30,000 lb. That still leaves 16,000 lb empty on the longest continental flight. That right there is beyond the 30% increase we are talking, so it's not crazy to think that airlines could switch over to a greener fuel on flights under certain distances. They'd have the capacity.