To answer this question, we need to know how such tools work.
A link shortener takes the link you want to shorten, wrap it and give you a short version for usage.
What happens after? You add this short link where needed: on Facebook, Google, any other traffic channel, your landing page, etc.
Once the link is called, it is unwrapped in the browser to the original one.
Everything seems to be smooth like this. So what are the dangers? 
The problem occurs when you need to use any other third-party tool for analytics. Why? The analytics tool wants you to add the dynamic parameters to the URL (utm, sub, affsub, etc.) and bitly cannot parse them properly.
Let’s take Facebook tracking as an example.
Option 1
You have added the parameters string to the URL parameters section and have added the shortened bitly link to the website URL:
The visitor decided to click on your ad. Now, what happens?
Facebook adds the parameters to the bitly link automatically before someone click on it. It will look like: bit.ly/2KEOXNx?cmpid=5fa2b5cc203ddb00017efa3f&sub1={{ad.id}}
The parameters are already added and the macros are replaced with the real value by Facebook. For example bit.ly/2KEOXNx?cmpid=5fa2b5cc203ddb00017efa3f&sub1=556578754
Now, when the real click is happening, the visitor is being redirected to the unwrapped version hiddening behind bit.ly/2KEOXNx.
Let it be something like https://yourdomain?utm_campaign=yourcampaign
The parameters added to the original bitly link are lost at this moment and you cannot use them further for analytics, automation, etc.
Option 2
Instead of adding the parameters string to Facebook, you decide to add them to the original link, wrap it with bitly and add only the bilty link to Facebook.
What happens here? Facebook is trying to pass it’s values to the bitly link during the click, it is added to bit.ly/2KEOXNx but once it is unwrapped in browser to https://yourdomain?sub1={{add.id} }, the {{ad.id}} is not replaced with the ad id provided by Facebook as the parameters are lost at the moment the bitly link is unwrapped.
So the working solution in that case (if for some reason you need to use bitly) is to add the ids directly to the link before you wrap it. But this means a lot on manual work as different ids are to be added to different ads and adsets.