I don't whether this idea is tangential or parallel, but we have a similar problem when we use the R number alone to describe contagiousness. A pathogen with an R number of 2 is far more contagious than another with an R number of 3, if the generation time of the former is a week, but that of the latter is a year. The timescale of the effect is essential when describing contagiousness, but I'm not sure I heard anyone in the media ever quoting generation times. Perhaps it wasn't so relevant for Covid if its generation time was stable, but it is necessary if you want to convert the R number into a growth rate, which I think is a more useful piece of information.
Strictly speaking, I wouldn't say R=2 with a shorter generation time is less contagious than R=3 with longer generation time, because contagiousness is typically defined in terms of secondary transmission events rather than timescale. But as you note, growth rate would be larger and hence would reach more cases sooner (even if overall epidemic might be smaller). This tradeoff between generation time and R was often an issue for new COVID variants, because wasn't initially clear if growth was coming from higher transmission at individual level, or shorter timescale, e.g. this paper we had on Delta: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8354568/
I don't whether this idea is tangential or parallel, but we have a similar problem when we use the R number alone to describe contagiousness. A pathogen with an R number of 2 is far more contagious than another with an R number of 3, if the generation time of the former is a week, but that of the latter is a year. The timescale of the effect is essential when describing contagiousness, but I'm not sure I heard anyone in the media ever quoting generation times. Perhaps it wasn't so relevant for Covid if its generation time was stable, but it is necessary if you want to convert the R number into a growth rate, which I think is a more useful piece of information.
Strictly speaking, I wouldn't say R=2 with a shorter generation time is less contagious than R=3 with longer generation time, because contagiousness is typically defined in terms of secondary transmission events rather than timescale. But as you note, growth rate would be larger and hence would reach more cases sooner (even if overall epidemic might be smaller). This tradeoff between generation time and R was often an issue for new COVID variants, because wasn't initially clear if growth was coming from higher transmission at individual level, or shorter timescale, e.g. this paper we had on Delta: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8354568/