Although I am only an amateur astronomer, the biggest disadvantage I see is that the Terrascope won't have the collecting area of a 150-meter telescope, as Earth is not transparent. We get the resolution of it, but we're basically looking through a very large atmospheric ring with what - >90% central obstruction? I cannot imagine the exposure times required to get anything meaningful and, also, the complexity of post-processing required to correct the ringing artifacts. Then, you're limited to just 1 square degree of sky to observe - unless you maneuver the Terrascope detector in orbit, which is prohibitively expensive due to the limited fuel. Imagine the slew times measured in months... Finally, it's going to have shorter mission design lifetime, if compared to a ground-based telescope. It can possibly be extended with a refueling mission, which would add to the cost, however. I think the overall value of this instrument is rather low, a curious proposition, but why?
I think the initial part of this snippet answers the question: this is mostly an effort by someone to type up a fun idea. Said someone is most likely a theorist, who doesn't let small details like slewing speed or exposure time prevent them from writing up a fun idea.
Honestly it seems like David Kipping could be a pretty fun guy to sit down and dream up weird stuff with, witness arxiv:1903.03423,
"The Halo Drive: Fuel-Free Relativistic Propulsion of Large Masses via Recycled Boomerang Photons"
"Abstract: Gravitational slingshots around a neutron star in a compact binary have been proposed as a means of accelerating large masses to potentially relativistic speeds. Such a slingshot is attractive since fuel is not expended for the acceleration, however it does entail a spacecraft diving into close proximity of the binary, which could be hazardous. It is proposed here that such a slingshot can be performed remotely using a beam of light which follows a boomerang null geodesic. Using a moving black hole as a gravitational mirror, kinetic energy from the black hole is transferred to the beam of light as a blueshift and upon return the recycled photons not only accelerate, but also add energy to, the spacecraft. It is shown here that this gained energy can be later expended to reach a terminal velocity of approximately 133% the velocity of the black hole. A civilization could exploit black holes as galactic way points but would be difficult to detect remotely, except for an elevated binary merger rate and excess binary eccentricity"
More generally, the high-res-low-collecting area setup is already hugely valuable in interferometers. This is, in a sense, a _very_ long baseline interferometer.
Presumably we'd want solar sail tech to be a bit more mature before doing so, but Ikaros has already demonstrated the viability of attitude control via dynamic reflectivity.