I usually start collecting once I reach $1K.
But today was tortuous. I reached the $1K level only to have a meeting reminder pop up (I had the day off of work, but people still send me tons of requests). That kicked me out of the game. I curse a few times, try to turn off reminder items and start again. I get to around $800 when another dang reminder comes up and kicks me out. I turn off more items and start again. Patience is wearing out and some of my best neighbors are gone (tapped 3 times - I did collect some money before crashing each time). This time I'm at $500 and now one neighbor's Springfield causes me to crash. I verified this by going into it a few times without any money built up and each time I crashed. So that person was deleted as a friend. But by now hours were wasted. So I just collected the remaining amount normally.
Given my difficulty of notices, texts, calls, and crashing Springfields, I applaud those who get to $2K or more per tap. I've even had my game crash after just 3 taps (meaning EA server issues). It must be a combination of finding the right Springfield to get the bigger tap value and some luck. I've tapped for around 30 minutes in what appears to be a good Springfield with premium items only to get around $600.