Why Somerville going ashore at Mers-el-Kebir might have backfired

Could Somerville have improved the outcome at Mers-el-Kebir by going ashore to negotiate personally?

Perhaps slightly, but it was unlikely to change the refusal and might instead have exposed the ultimatum as a bluff while giving the French more preparation time.

A face-to-face meeting between Somerville and the French command might have helped at the margin, but it was unlikely to overcome the refusal. Going ashore could also make the British ultimatum look like a bluff. The meeting would give the French fleet more time to prepare for action. Personal diplomacy was a real option whose operational risks may have outweighed its uncertain chance of success.