They make the schedule so long in order to maximise tv revenue. Showing two games at once isn't as valuable as 2 games on 2 different days. The issue then is it drags on and add in the "India" clause of India not getting knocked out early for the sake of sponsors, we end up in this mess.
You could do a qualifying tournament for minnows, but no TV money in that and extra expense for the hosts. You could cut the 2 groups down to even numbers - 6 in each. Means they play once every 6 days as a minimum and group stages would be limited to 30 days. If you went for 2 games a day, scheduled at 10.30pm and 2pm to minimise overlap you could get it down to 3 day turnaround and 15 days for the group stages. Remember, far less travelling in the UK. Stick to the same schedule and Qtr Final is Day 18, Semi Day 21 and Final Day 24. That's a 20 day saving, two associates included and only a slight overlap in matches.
If you went to 16 teams, then it's once every 4 days you play or 28 days for group stages. Stick to 3 days for Qtr/Semi/Final and you are done by day 37.