The continuous line advice is a persistent myth that is easily disproved even in the videos of those who recommend it.
It is impossible for the unicycle to maintain a leaning forward position without very quickly going to UPD. For any stable system, the centre of mass must be over the point of contact. In theory it can be done by having both the body and unicycle vertical but this results in directional instability due to the lack of trail in the steering geometry.
All forwards riding is done with the body slightly leaning forward and the uni slightly leaning back. This geometry overcomes some of the tendency for the pedalling to rotate the uni around the vertical axis.
This was discussed at length in this thread. The first post includes a link to a video that recommends it and in another I point out where the rider brings the uni into the normal leaning back position immediately after taking off.
I also invited anyone to find a photo of a rider with the uni leaning forward. None were provided.
I explained that leaning the uni forward with the body is a starting out situation to get initial momentum from the “fall” and the uni is brought quickly underneath to counteract it. I think I also posted that on the thread with the video.
When I taught my sons to ride they commented that the advice to get the uni leaning backwards after taking off was a really important piece of advice. My elder son was riding ten metres across grass after half an hour in the saddle.
Novice riders need a substantial lean or they will not be able to control direction. I can’t see how much lean SpinningWoman has from her video but directional stability is clearly an issue for her.