When I learn a new song I like to put the metronome faster by about 5 to 10 BPM. Lets say the original song is at 100 BPM I will practice the song until it sound good at 110 BPM on the metronome. After that the song feel easier at 100. This trick help me to feel comfortable with a song faster.
I do that also. I use an app called Tempo Slow which allows you to play the song at a faster tempo without sounding like chipmunks. I might try and see how fast I can play an already fast song. Time Won't Wait by Jamiroquai is a recent example. I can technically keep up with it at 125% of original tempo but it starts to lose its groove. I also found I should use it sparingly because I have found that some songs sound better at about 110%. Then when I need to play it normal tempo, it feels like its too slow. It's still really fun though.
I find it makes me rush the tempo. I will usually learn it very slow, like crawling slow, until I get the fingerings down, then I speed it up to tempo, but never faster. That just me.
I prefer to learn the song from the original tempo from the start, not faster and not slower. For myself at least I think that is how I learn the song best at shortest possible time in therms of getting the tempo and groove right from the start. I rarely even play difficult passages slowly at first because sometimes I can find that even harder than full speed cause I wont get that feel, you know when you just feel it from the heart and straight out in the arms, start involving the brain and its a whole lot more difficult
I practice above tempo if the song is already difficult AFTER I can play it at tempo, it makes it that much easier since tempos almost always get higher live