If you can afford to have procedures spread out, then yes, it makes sense. But each trip to the operating theater, and the subsequent nights in hospital, can be costly all on their own. And, of course, some of us just can't wait. All that said, splitting the work into two parts is definitely the wiser course.
I was in hospital for a week, and it really made it easier on everyone -- I had my mom and my partner at the time with me, so they also got a break. Xanax was prescribed to keep my anxiety in check, and the good pain meds were readily available. The staff made sure I had cold-packs regularly strapped to my chin and forehead -- the soft ones, with a layer of gauze in between to protect the skin.
The only transitioner I recall meeting while there was a man who'd just gotten his balls and metoidioplasty. He'd been on T for years and years: full beard, deep voice, even his hairline had begun to recede. He was about ten years older than I was. Felt like a mentor, actually. I was complaining about the pain, and he pointed out that this was nothing compared to dysphoria, and that we were simply trading a life-long pain for a short-term pain, which would then be over and forgotten. Great guy -- wish I'd remembered his name.
I recall that pain I was in, the second night after surgery. Not just brutal -- it was excruciating, and I wanted to die (in came the Xanax and Oxy), and an angel of a nurse helped talk me down. "You're going to be so beautiful!" she said, and I held onto those words. Today, it's all a distant memory. No longer sharp. Rather fuzzy, in fact, or perhaps foggy... but I still retain an understanding of what 10 out of 10 on the pain scale means now.