Having buttonmen in the restaurant would have been the equivalent of Michael entering the meeting with a gun; it would have alerted Solozzo that something was up, and the plan never would have worked.

The only way to do it was totally by surprise; Michael, the least threat to Solozzo, entered the meeting alone and unarmed. Solozzo was already on the run, fearing for his life, and so the slightest hint that anything was up would have been disastrous.

That's why Solozzo requested the meeting with Michael -- because he knew that Michael was a civilion and was not involved in the business. Anyone who posed any threat to Solozzo would have been treated with a lot more suspicion. In fact, look how suspicious Solozzo is of Michael despite Michael's unthreatening status.