I think you have a slight misconception of how a feeling of rest is given in music. Yes, baroque music did have the tendency to just go on but that does not mean it could not have places of rest.
The effect of rest or pause can be given by just the use of a longer note value. If you have a piece in 3/4 time and it is mostly quavers and crotchet the use of a minim note will also give the effect of a rest.
So even if a piece has a "...a constant flow of music the entire time." that does not entirely mean it has no moments where a pause is present.
There is the issue of suspense also. If there is no gradually slowing down of music then the effect of a cadence is lost. There is a natural tendency to have a build up of tension as your phrases near its end and then a release of tension when the leading tone resolve in the new phrase.
If there is mono tempo then it is not really possible to build and release this tension but as I say rest are not the only way to give this effect.
PS to the mods I realise that this answer is more to answer the misconception that the OP may have. The only reason why I did not comment is because of length.