Unfortunately this is not the case for a few reasons. The radio observatories in the US with visitor centers nearby have substantial problems with RFI among visitors. The receivers are extremely sensitive, shoddy electronics often emit outside their regulated spectrum, and the signal can be contaminated after it's been converted from the sky frequency to an intermediate frequency inside the electronics (often around 1 GHz) despite shielding. At Kitt Peak, observations with the VLBA station during the day are often nuked (esp. 2 GHz, "S Band"), and at the VLA many large programs aren't even scheduled when there will be many visitors. However this is known and acceptable because visitors are the lifeblood of the facility! It's a bit of a catch-22, because it means the facility is less functional, but it shows citizens why they should support the facility with their tax dollars and also support science in general.

For FAST, one must understand that this could not be smaller potatoes for the PRC, as big as it is. A hundred million dollars for a government project is a rounding error. However, the excellence of the design and it being the best in the world on some metrics has engaged the Chinese public in a huge way. Consider how popular space is with the public in the US and Europe, and that the PRC has not really had a world leading facility (Hubble, Keck/VLT, VLA, ALMA, etc.) to engage that latent interest. I have heard an anecdote from an astronomer that they have gotten so much bang for their bunk in this way, that the government may simply build a second one and keep the first for tourists!