This is a really neat way for web interaction. I have been using typeforms for a while, although i’ve noticed it has not picked up the way I expected it to.

One primary reason I feel is when an entire form is in front of you, you can mentally assess how much time it will take based on the number of fields to input.
When inputs are presented one by one there’s an unknown sense of how long this will go on for.
Which probably can be worked around by introducing a small progress bar (a small strip is enough).
Still, you’re not aware whether the next input will be a textarea asking for your address, or do you need to get your credit card handy etc.

The conversational seems to be an ideal fit for surveys, but I believe there might be a bit of paranoia when it comes to personal/financial information.