Do not rewrite the Deen to satisfy its enemies. You can follow your own rationality and logic, only in the absence of a clear hukm from Allah and His Messenger.
If you want a list of examples where Rasulullah ﷺ ordered the Hadd against those who slandered him, we can provide it.
It seems that those who do not understand avenging the Prophet ﷺ are those who do not know him adequately.
Do not apply the rules followed before the Hijrah and forget those commanded after it. SubhanAllah, the Muslims in Makkah were begging Rasulullah ﷺ for the permission to defend him, and the ayaat of Jihad came as a relief to them in Madinah.
Now there are those who cherish the state of passivity that the Sahabah hated.
You are worried about the image of Islam?
When they are allowed to make a mockery of Rasulullah ﷺ, when they are allowed to slander him ﷺ, and when they force us to accept that he ﷺ can be slandered and ridiculed; tell me, why after that will they take seriously the Message he was sent with?
Wallahi, Wallahi Wallahi, the hearts of more people will turn to Islam when they see the Prophet of Islam being defended, than if they see his followers tolerating him being slandered.
اللّهُـمَّ صَلِّ عَلـى مُحمَّـد، وَعَلـى آلِ مُحمَّد، كَمـا صَلَّيـتَ عَلـىإبْراهـيمَ وَعَلـى آلِ إبْراهـيم، إِنَّكَ حَمـيدٌ مَجـيد ، اللّهُـمَّ بارِكْ عَلـى مُحمَّـد، وَعَلـى آلِ مُحمَّـد، كَمـا بارِكْتَ عَلـىإبْراهـيمَ وَعَلـى آلِ إبْراهيم، إِنَّكَ حَمـيدٌ مَجـيد