I could imagine saying "it's been nice talking to you" as a speaker at a conference where "it's been nice talking with you" would require there to have been some dialogue. For example, a town hall meeting or open debate or a conversation between two people.

Yes, and you nailed it on the head when you spoke of permission vs. capability. Here's a conversation that I hear take place on a daily basis at public school that illustrates this point while also demonstrating that this distinction is a formality. Student: Can I go to the bathroom? Teacher: I don't know, can you go to the bathroom? Student (exasperated): May I go to the bathroom? Teacher: Yes but first tell me: how many years have you been asking me that same question and getting the same answer? Student: Three years. The teacher fully understands what the student means but feigns confusion for fun as much for its teaching value. The student has been through this many times before but still makes the same mistake because this situation is probably the only situation where the student is being asked to make a distiction between the two words. Part of the humor in this situation comes from how the phrase "go to the bathroom" is meant as "walk to the bathroom" or "leave the class to visit the bathroom" but when the question is rephrased as "CAN you go to the bathroom?" it sounds like a question a doctor or nurse would ask you. The student's peers in this situation interpret the teacher's playful rephrasing as an informal version of "Are you capable of defecation?" or "Are you capable of urination?" I think this double-entendre is the reason that this specific situation is so often singled out as a chance to teach the difference between "can" and "may". Many other situations occur where people use "can" when they really mean "may." For example: Can I have it Mommy? Can I help you? (this one could go either way actually) Can I take your coat? Can I go to the Movies tonight? Can anybody else offer some good examples where "can" replaces "may." With this last use of "can" I really am using it in the sense of "are you capable" despite the fact that I am sure other English speakers are "capable" of providing more examples. I also realize I have no authority to tell them what they may and may not do. What I'm really saying is "Will someone else offer some good examples where "can" replaces "may."

There's nothing wrong with the answer by sjwoods but I'd like to offer other ways I would prefer to say this:

My French for your English! In London

I'm 27 years old. ["girl" sounds like you want to imply some immaturity to me, this conflicts with the education you reference] I come from the French part of Switzerland (Geneva) and studied political and social sciences. I'm very curious and interested in many things such as culture, food, art, travel, etc. I like to meet new people. I will be in London for one more month! I'd love to find someone I could meet with maybe twice a week to practice my English and my accent! We can speak part time each language! I'm learning English because I need it for everything and I really like it too. I'm a native French speaker who'd love to help someone with his French and maybe know more about French culture! I'm looking for someone nice, available twice a week and who would like to speak about everything and nothing!:) Let me know!!! I'm waiting for your answer! Hope to see you soon! Virginia

 

I completely agree with the idea that there is no one thing that will make all other needs unecessary but I believe the following idea from Eric Hoffer makes the argument that love in the form of compassion is the closest thing to making this Beatles quote a reality because from compassion (and community without which compassion does not exist) all other needs are provided. Here's my paraphrase of the Eric Hoffer idea:

Justice, law, humility, courage, selflessness, etc., all these noble characteristics can be perverted by carrying them to the extreme. Only compassion, the ability to feel another's needs and act on providing them, is uncorruptible.