Trouble with that plan is 1) Sol and McCluskey would not have been there had the meeting not taken place, and 2) if you have the meeting under those circumstances, you put Michael in direct danger, which was unacceptable.
To your underlying point, of course it was personal as well as business. If it was *strictly* business, Michael would have never offered, much less insisted, on being the triggerman, even though it was the most effective assassination plan feasible at the time.
The only way Solozzo and McCluskey would even be seen in public was at the meeting with Michael, so only he could shoot them. Of course he took what they did personally, but killing Solozzo was stricyly business because as Michael explained, the "key" for Sol was killing Vito. As you may recall Vito told Sol he could do whatever he wanted so long as he did not interfere with the Corleones. Sol decided not to take that advice.
