I actually think this is a really good--albeit not necessarily
ideal--strategy to wait until round 2 for your top choices.
I only did 1 school round 2 (Yale) and my essays were head and shoulders above my round 1 essays. It's amazing what a few months can do to foster additional reflection and comfort with the MBA admissions process. I literally wrote my Yale essays one morning on a whim at work, made some minor edits, and was good to go. My round 1 essays, by contrast, took a lot more planning and were still not as fluid or compelling as my Yale essays (but perhaps this was some subconscious sign that Yale was the best school for me all along
).
Now, this strategy wasn't really
intentional on my part--after receiving admission to Darden and striking out at Sloan, I basically decided that I really wanted a better chance at New England option. I really felt I had made a mistake not applying to Yale before because I kept having that "what if" feeling--I liked the curriculum, the students, the social impact focus, the location, etc.
I realize that my situation isn't necessarily representative, and it certainly isn't exactly the same as yours, but here's how I'd break out the pros/cons for round 2 (assuming you apply to a few "back-up" type schools in round 1):
Pros:- as you mentioned, your essays are likely to be better
- on a less tangible level, you're more likely "get" the admissions process and how to present yourself in both your application and interview
- having an admit from a lower-ranked school (that you'd still like to attend) gives you security and can boost your confidence for round 2 applications
- you buy yourself extra time, generally without a penalty (as kingfalcon said, round 1 and 2 admissions for Sloan and most other schools are about equal in terms of selectivity/competitiveness)--and particularly if you're a young candidate, this few months could make a huge difference in terms of a promotion or additional project that you could mention
Cons:- you drag the process out longer
- if you don't get into your round 1 schools, your confidence may take a big hit
- if you do get into a round 1 school, you will very likely be in the position where you make multiple deposits (as I was) because you have to secure a spot at a different school before hearing from Sloan/Stanford
Bottom line: you can definitely make an argument for either. If I could do it again, I personally would’ve done more round 2s and given myself a bit more time to develop my story. Good luck!