Answering as a non-astronomer: Arecibo had two major advantages over synthetic aperture arrays. The first was the "seeing" power or total sensitivity. Because it's a large single dish it collects far more photons than multiple smaller dishes.

The receivers were also cooled with liquid helium IIRC so the noise floor was ridiculously low. Those features combined made for not just high resolution but high sensitivity observations. Most telescope arrays (to my understanding) have a higher noise floor.

The second feature was the ability to transmit. Arecibo has been used for decades as a radar to image asteroids and such. Many asteroids are too small and dark to effectively image with optical telescopes where Arecibo's radar is no problem. It also gets extremely accurate distance and rotation measurements.

For those interested: FAST has a diameter of 500m, compared to 300m for Arecibo (https://en.wikipedia.org/wiki/Five-hundred-meter_Aperture_Sp...)

There’s also https://en.wikipedia.org/wiki/RATAN-600, with a diameter of 575m, but that isn’t a fully filled dish.

Though, as the linked article explains, you can’t use the entire 500m as a single aperture. You can only use 300m of it at a time, but you can “point” it in different directions by using different 300m windows.

I studied pulsars in University and worked with Arecibo, Green Bank, did some data analysis with VLA, and worked on some undergrad projects using low frequency arrays.

The details get complex, but the gist of it is that arrays let you see bright small scale things, while single aperture telescopes let you see large scale that are dim.

Additionally, an array suffers with sensitivity and noise issues if they don't have enough antennas covering discrete distance pairings. This usually occurs at short baselines since array elements often have a minimum spacing. Single aperture telescopes have a large instantaneous gain factor due to their large collecting area, which is really hard to make up without an exceedingly large number of array elements. For example, Arecibo has the same collecting area as ~148 VLA dishes.

Data handling for an array is complex as well, as you need to mix and process the data from each telescope to sync them together (correlation), while a single aperture telescope doesn't need this step.

On the other hand, an array is generally much less sensitive to instrument noise as the cumulative signal means noise from a single array element has a much lower impact overall. Also, it generally dodges the single-point failure modes by being essentially redundant. You can still operate with one or more elements missing/out of action.

Each telescope type has it's pros and cons, and there are equally valid use cases for each one.

One thing that I imagine is quite difficult to perform on an array is the type of planetary radar Arecibo specialized in by nature of it's high-power S-Band radar (2.38GHz). With AO's S-Band radar, it was possible to get highly detailed imaging and orbital parameters of near-Earth Asteroids with short observations, while determining orbital parameters with optical observations can take numerous observations (and doesn't generally give you the same detailed 3d models). NASA's Goldstone Observatory is the next best telescope for this, but is nearly 20x less sensitive due to it's size and different operating frequency.

While maximum resolution is limited by the diameter or the largest baseline in an array, there is one advantage to single dishes: There is no lack of small baselines. Which implies that you can only really get images of large, dim structures with a single dish.

Also sensitivity is given by total collecting area, which is very competitive for a single huge dish compared to a limited number of small dishes.

Arecibo was initially built to excite plasma balls in the atmosphere to study them, and was also used for other transmitter uses that required a super powerful transmitter, initially designed for that plasma use.

Built to “excite plasma balls” sounds like it would be creating plasma balls if it’s own. It was used as a scatter radar to study plasma in the upper atmosphere.