The change in radius of a black hole when 1 bit of information is added is much smaller than 1 Planck length. The Planck length is just a convenient unit of measure in physics. It has no relevance to limits of space or time at all.

Here's an article on the subject:

https://www.quora.com/Is-there-anything-smaller-than-a-Planc...

Interesting. I am now better informed.

Why would the Planck length be the smallest measurable length in the universe?

Edit: To be more clear: Is there a theoretical reason why the Planck length would approximate the smallest measurable length?