There's a saying that I think would apply here: It's better to ask for forgiveness than to ask for permission. I think this applies almost doubly for Roleplayers in this type of environment. If you happen upon two people in a tavern having a conversation it's far easier to try to engage them and be ignored than it is to ask to join and potentially be ignored. The fear or rejection tends to be stronger than the desire to engage in most cases. Maybe I happen upon your RP and see a perfect opening to get involved myself, so I send you a /tell to ask permission to join and you guys post two or three more times before responding, even if it was favorably chances are that window of opportunity I had has come and gone when you continued your scene.
Regardless however, many people are hesitant for one reason or another about engaging in RP with people they don't know, and it adds an extra level of hesitation when you're expected to ask for permission prior to joining. If you're going to RP in public you should just do so operating under the impression you're sending an invitation to anyone around to join you, otherwise you need to be doing your private RP in private. Not to mention how much requiring permission breaks immersion. Have you ever sat in a cafe or something and overheard a conversation, and then walked up to one of the people involved and whispered in their ear "Hey do you mind if I join your conversation?" I'm going to guess the answer to that is no. That would be incredibly creepy.
Regardless however, many people are hesitant for one reason or another about engaging in RP with people they don't know, and it adds an extra level of hesitation when you're expected to ask for permission prior to joining. If you're going to RP in public you should just do so operating under the impression you're sending an invitation to anyone around to join you, otherwise you need to be doing your private RP in private. Not to mention how much requiring permission breaks immersion. Have you ever sat in a cafe or something and overheard a conversation, and then walked up to one of the people involved and whispered in their ear "Hey do you mind if I join your conversation?" I'm going to guess the answer to that is no. That would be incredibly creepy.