Yes, this is both practical in the real world and very common. Almost all trans-Pacific flights do this (called "step climbs") because they start off much, much heavier than they land. Their initial cruising altitudes need to be relatively low due to their high initial weight, but they're able to climb up into the thinner air once they've burned off hundreds of thousands of pounds of fuel weight and that enables them to fly the remainder of the flight more efficiently.
This is much less common on short 2-hour domestic hops, though. Those typically aren't altitude-limited by their fuel weight in the first place, so they have no need to start off at a lower altitude and then climb later. They just climb straight to a cruising altitude that they'll use all the way to top-of-descent unless they or ATC need them to change altitude for something like weather, turbulence, or traffic. The fuel weight is a much smaller fraction of the overall aircraft takeoff weight on 2-hour domestic hops than it is on 15-hour trans-Pacific long-hauls. This is also why those aircraft can typically land immediately after takeoff if needed and typically don't even have fuel jettison capabilities.
Here's an example of a Tokyo-Narita to New York-JFK flight on a Japan Airlines Boeing 777-300ER earlier this week:
This flight is a bit over 12 hours in duration. It started off with an initial cruise altitude of 32,000 feet. Interestingly, it seems to have initially received a block clearance, taking nearly an hour and 40 minutes to climb from 30,000 to 32,000. It then did a step climb to 33,000 at roughly 3 hours, 34,000 at 4.5 hours, 35,000 at 6.5 hours, and finally 37,000 at 9.5 hours. If you are paying attention as a passenger, you can hear when these step climbs take place, as the engines will get noticeably louder for several minutes or so during the step climbs. Of course, you can also see it on the flight tracker on the in-flight entertainment screens on flights that have those.
Because you can always lower your pitch angle, and get less drag and save fuel. In this way, you don't need climb to consume additional fuel. And you don't mess with other airway traffics.
This is what you'll do to maintain an altitude assignment as you burn off fuel (generally done in very small steps constantly and automatically by the autopilot.) It does reduce fuel burn somewhat, of course, but it doesn't reduce it as much as climbing into the thinner air does.