Why don't people just apply to every MBA program in the top-20?

I applied to 8 schools this past cycle it was almost a full-time second job. Additionally, when it comes time to interview, I was having to fly out two to three times a week - which is a huge burden, whether you are working full time or not. My opinion is that applying to 20 schools would be nearly impossible to execute while maintaining quality, even with the most dedicated effort - you are likely underestimating the time and care you need to put into each application. In sum, consider:

1. Crafting essays that are introspective and powerful, taking the time to write and re-write them. This takes a ton of time.
2. As you mentioned, letter of rec burden. Not all schools are on standard, and 20 schools IMO would be an unreasonable ask. I felt bad about asking for 8, even with the standardization across some schools.
3. Assuming a decent hit rate, and even interviewing across multiple rounds would be a HUGE burden. The flights, hotels, food - everything - all comes out of your pocket, and the interviews often hit near each other. Think about keeping each school's facts in order across possibly 20 interviews, when you can have three or so in one week, for multiple weeks on end.
4. Connecting with current students / alumni across 20 schools would be very difficult. Same if you try to visit. I would recommend doing both of these things if possible.
5. Multiply approx. $200 times 20 - that's just the application fees.
6. Not all schools are the same just because they are in the top 20. There are truly distinct differences between top B schools, and many will not mesh with your goals and interests. Spend the time figuring out which schools align best with what you want to get out of the experience. If you are not truly engaged with the school, and passionate about why you want to attend, it will come across in your essays and interviews.
7. Finally, all of this needs to be done while working a full-time job (presumably)!

My advice would be to strengthen your profile so that you are competitive at your goal schools, and shoot for a list more along the lines of 4-8 schools, ideally across rounds 1 and 2.