The biggest issue is the sheer separation required. EHT operates in mm wave light, visible is 4-6 orders of magnitude shorter wavelength. There are several smaller scale interferometers. They can already do quite impressive things because even a 50m baseline is better than any optical telescope that exists.
The way that timing works for EHT is each station has a GPS reference that's conditioned with a very good atomic clock - for example at SPT we use a hydrogen maser. The readout and timing system is separate from the normal telescope control system, we just make sure the dish is tracking the right spot before we need to start saving data (sampling around 64 Gbps).
I'm not sure what the timing requirements are for visible and how the clock is distributed, but syncing clocks extremely well over long distances shouldn't be insurmountable. LISA needs to solve this problem for gravitational waves and that's a million+ km baseline.
Some problems go away in space. You obviously need extremely accurate station keeping (have a look how LISA Pathfinder does it, very cool), but on Earth we also have to take continental drift into account.