Why not a satellite-based telescope to observe Mercury in the thermal infrared?
Space-borne satellites that are designed to look at the Sun (e.g., SOHO) aren't instrumented to look in the thermal infrared, while satellite-based telescopes that are instrumented to look in the thermal infrared in general don't point anywhere close to the Sun.
One issue with imaging Mercury from roughly one AU is accidentally imaging the Sun. Hubble was rarely allowed to point to Venus, but never Mercury. Another issue is cooling. Even if the telescope isn't directly imaging the Sun, key unshielded portions of the satellite will inevitably be facing the Sun while imaging Mercury. Thermal imaging satellites need to be cryogenically cooled. Pointing a space-based thermal imager at Mercury would reduce the vehicle's usable lifespan.
Neither of those issues (accidentally imaging the Sun and heating problems) is an issue in the case of satellites sent to Mercury. To date, only two satellites have been sent to Mercury (Mariner 10 and MESSENGER) and one is on the way (BepiColombo). MESSENGER was not instrumented to see in the thermal infrared. Mariner 10 was and BepiColombo is. Mariner 10 made three flybys of Mercury in 1974 and 1975. These included observations in the thermal infrared, but the received data were limited.
*Why not a ground-based telescope to observe Mercury in the thermal infrared?*
There would be so much thermal infrared airglow when the Sun is below the horizon so as to make observations of Mercury worthless. There would be too much of a chance of accidentally imaging the Sun when the Sun is high in the sky. Cooling is of course an issue as well.
The above do not apply if path of a solar eclipse happens to pass over a thermal infrared telescope. Exactly that happened in July 1991, when Mauna Kea observatory was almost exactly in the center of the path of totality. The infrared telescope at Mauna Kea was most definitely put to use during this eclipse, but not to look at Mercury. Apparently observing Mercury wasn't given a high enough priority.
*Why not SOFIA?*
For one thing, it's construction is suboptimal for this usage; see the other answer. For another, it's too valuable. SOFIA's predecessor, the Kuiper Airborne Observatory (KAO), was used twice to observe Mercury in the infrared. The aircraft's fuselage protected the telescope against seeing the Sun. However, because of the possibility of pointing errors that might result in imaging the Sun, these observations were made at the end of the KAO's life. (SOFIA was about to replace the KAO.) SOFIA isn't yet at the end of its life.
*Why during an eclipse?*
Solar eclipses provide unique opportunities for observing the Sun, and also apparently for observing Mercury. Solar eclipses have long been accompanied by numerous scientific observations specialized to take advantage of the eclipse.
It doesn't have to be done during an eclipse. Mercury does need to be fairly high in the sky to be able to see it in thermal infrared, even at the high altitude at which NASA's WB-57s fly. A total eclipse is not essential for this experiment. The personnel and aircraft are being used to observe the Sun during totality, and this apparently conflicts with the Mercury observation experiment. The Mercury observations instead are being performed 30 minutes prior to and after the total eclipse.
Being a one-off experiment, and being a secondary experiment, (the primary experiment is observing the Sun), the possibility of accidentally imaging the Sun is not a complete disaster. The Sun will still be partially eclipsed by the Moon during that period. This will reduce the amount of secondary light (solar thermal infrared absorbed and reemitted by the atmosphere, eventually reaching the instrument) compared to that which results from an uneclipsed Sun.