You learn something new every day.
I've accidentally hit the connect button on my phone many times and cringed, knowing the request wouldn't be personalized.
Many people will tell you they delete non-personalized LinkedIn connection requests.
In an INC article (link below), a solution is offered.
I went ahead and took some screenshots and added them below to add value to your day.
On a desktop, it's easy to customize the connection request. You can go to the person's profile page and use the "connect" feature.
While I don't think this is the only factor in that decision, it does come off as lazy when you get one without a note.
However, when you visit a person's profile on the mobile app and hit the same "connect" button, it automatically sends the default text invite. What most mobile app users don't know is before you hit "connect" in a person's profile in the app, you need to hit the three tiny dots in the upper right corner of your phone screen...
which produces a set of options that includes customizing the connection request.
This little-known feature could help you dramatically increase your connections requests when using the app.
There's more in the original article. Check it out.