Given this is 1960's technology - land lines, no software, and all the banks of screens you see in 'Houston' are tv monitors, NOT computers, everything was done to a pre-prepared script. Precision was absolutely key. For example, in docking and undocking. Think about it, Collins orbiting the Moon whilst the guys were 'collecting rocks' needed to be in exactly the right place at the right time for when the capsule took off from the Moon, etc. So, ditto, the "live" tv broadcast. Had there been a satellite geopositioned (=at the same speed of orbit as the Moon so that in effect, it is stationary to it, per position) nil problemo. But it had to ensure a localised satellite was ready in place at the right time - how incredibly logistically efficient would one need to be to have it there just when you need it?
And then Richard "Tricky Dicky" Nixon ringing Apollo by landline and chatting to the astronauts in person...yes, radio technology was absolutely marvellous: signals bouncing from one station to another to make this possible... Yes, mate! It's possible if we all just think hard enough.