As someone who likes making analyses from random datasets, I have a few issues with these types of services:
1) There is often no indication of the distribution rights of the data, or whether the data was obtained ethically from the source (i.e. following the ToS). I made this mistake when I used an OKCupid dataset released on an Open Data Repository; turns out it was scraped with a logged-in account and the dataset was taken down by DMCA
2) There is no indication of the quality of the data, and as a result, it may take an absurd amount of time cleaning the data for accuracy. Some datasets may not be salvageable.
3) Bandwidth. Good datasets have lots of data for better models, which these sites may not be able to support. (BigQuery public datasets solve this problem however)