Eventually, AI will be indistinguishable from real humans, and at that point, I won't see anything wrong with it. However, as it is right now, AI is not advanced enough.

Also, the biggest problem I can see is people falling in love with a proprietary AI, and the company that operates the AI can arbitrarily change the AI's parameters which would change the AI's personality. Also, if the company goes bankrupt or gets sold and the service ends, the people who got into a relationship with the AI would be heartbroken.