It makes sense for an interstellar flight though. If you want to leave the solar system doing say 30Mm/s (i.e. .1c) you expend less delta-v doing a slingshot around the sun than accelerating directly from Earth.
Longer: Oberth effect says you want to do the thrusting at max speed, not "deep in the gravity well". Often they coincide but they're not the same thing.
Even longer: If you want to use the Oberth effect, you want to go into a highly eccentric elliptic orbit with a low perigee. (Ie non-circular.) Then you do your thrusting at the perigee. Your apogee is still at high altitude. The perigee burn happens at high speed and actually raises the apogee.
You can think of it this way: if you shut down your engines right now, you are in an orbit that returns to the same point. So perigee burns can only raise apogee and apogee burns can only raise perigee. (If we talk about elliptic orbits.)
Mercury is in a low circular orbit. It does not really help to go to an orbit with a low apogee, with the ultimate goal of raising apogee!
You might use a sun slingshot by lowering your perigee but your apogee would still be at earth orbit. That would mean you would cross Mercury's orbit, but with a very high speed. You couldn't stop at Mercury (match speeds with it). Then you'd do a quick high thrust burn at high speed near perigee.
All this is in vain though since for 0.1 c magnitude velocities (30,000 km/s), if you had humans, you would have to thrust for weeks to keep acceleration below say 2 g and the gravity slingshot would be meaningless anyway as the speeds are so low, these are phenomena from totally different worlds. Earth's orbital velocity is 30 km/s and Mercury's 60 km/s. Thousand fold difference.
It's like saying building rocket launchpad on a 300 m high hill is useful since you're then closer to space.
The particular application would be for the export of fungible goods from the vicinity of Mercury to the rest of the solar system. Solar sails could be used to enter a solar orbit with a low pedigree to maximize thrust from the solar sail. This would still involve very long transit times and either the use of gravitational slingshots or multiple passes by the sun. It might make more economic sense to export energy as beams of microwaves.
