Unfortunately, I have to agree with Shams Juma on his answer of "it depends". However, there are a few pieces of information you should also consider while making an informed decision about a phone number field.
First and foremost always remember user intent when considering fields to add or remove in any form scenario. If any user, regardless of age or any other pertinent demographic information, suspects that giving their phone number will cause an unwanted phone call after the application process is over, there may be some reluctance on the users part to provide that information. It's a classic case of negative cognitive bias that can produce immediate anxiety with just about any set of users (just as you mention in your question as a "con").
The next question is, how critical is the phone number in terms of completing the application process? I just wrote an article about form optimization and one thing I stressed with consistency is being hyper critical of any fields that are considered to be optional and/or not required. One area I've found success is putting additional or non required fields directly in plain view on the thank you page. This can reduce friction amongst any user persona and giving them the chance, IF INTERESTED, to allow you to contact them after the process is complete. You can also choose to incentivize them to help participate as another answer mentions above on the thank you page without interfering in the application process. One thing that's consistent about most user groups (and there aren't many consistencies) is that most people aren't thinking about giving you feedback during any part of their customer journey. More than likely it's one of the farthest things on their mind.
Researching the combined psychographic and demographic data sets is important to identify "potential" friction and anxiety points, but don't get too wrapped up in it. You can use it as a baseline for your hypothesis, but I have seen hundreds of cases where extrinsic factors completely override any buyer modalities or personas or whatever you want to call them. Also, they can be counter productive to an agile marketing solution and the ability to move quickly to rule out what works and what doesn't. It's usually very beneficial as an ongoing documented process when you start to understand your user better and establish a baseline control that you will continue to test against.
The best thing about this entire process is, it's a continual test to find out what works. If you are debating on whether or not to put the phone number field in, try it, test it (and I will explain how here in a second) and figure out if it worked or not. Worst case scenario is you know what "NOT" to do going forward. In the world of conversion optimization and user experience, best practices are a thing of the past. In fact, worst thing you can do is to listen to a bunch of "experts" spout out best practices. If anyone gives advice regarding "best practices" completely ignore it as they have no clue to what they are saying.
Once you decide to include it in your first round of testing, make sure you have realtime inline validation on all your fields, as well as a link below or to the side (again test placement as well) setting an expectation on why you are asking for a phone number, just like another answer mentioned previously.
If you have the traffic and you can segment your users, by all means setup an A/B test. Most people assume that most sites have enough traffic and conversion data to do so, which is also rarely the case. If you don't have enough traffic, use a qualitative approach and setup a tool that records user visits like HotJar for viewing. It's about as easy as they come to install and it's very affordable. You can also set it up to only record the page that the form is on, so you maximize your time to just looking at videos where users are on the page where your form exists. There are other behavioral filters you can implement with HotJar in order to save time when reviewing videos as well. If you really want to get crazy combine HotJar and Formisimo together and you may very well get enough quan/qual data in order to feel comfortable with your decision. This is something I would definitely try before going down the A/B testing route especially if there is any doubt about having enough traffic to gain the right sample size.
Let me know if there is anything else I can help you answer. Good luck and would also love to know how it turns out. Thanks.