Roast my idea!

It's challenging to get customers to provide feedback at all. I'd hate to sour relationships with people willing to provide feedback by creating a bad experience with a bot.

Is the idea that the bot would be available at times when I'm not? If that's what you're after, I'd want some solid numbers. When I'm trying out a new product, I don't mind that communication being asynchronous because it's unlikely that my issues will be resolved immediately anyway. If you could do an A/B test demonstrating that people are happier talking to a bot immediately than having a delayed discussion with a human, that would be a compelling reason to buy.

It's a great idea in theory. I've just had a hard time engaging users to participate and provide feedback unless it's something subjective to their purview only if that makes sense.

Sounds worthwhile but I'm against it. I got a few reasons to say so.

1. It's gonna be costly. A lot of requests need to be made just to finish a single conversation. It might make sense for a tiny fraction of people/businesses but you might not get traction.
2. AI is not very good at being context aware. You're saying you'll answer questions & ask feedback with same chat. It will most likely mess up on learning from it or might struggle to make sense of conversation.
3. Since it's costly. People might just choose to interact with customers directly since they're not gonna need to interact with everyone, only the highly invested ones.

But I'm still planning to make similar kind of chat bot as a service too(This is not copying I wanted to do this for a while) when I make some time :)
If you're still planning to make it. Do check out a prototype to see if it's responding properly in context.

Finally, Good Luck

Developing a chatbot to automate client contacts & collect data seems like a really worthwhile idea. Give users a little additional information about the features & the advantages. Put a light on how chatbot can precisely solve issues.