Again though, you are still comparing clubs hisorically, players don't do that in the same way.
In the last 15 years, Arsenal have provided the premier league with many more World Class signings than Liverpool have. Most of Liverpools prominent players during this time have been academy players like Owen and Gerrard.
The reality is that when Liverpool had Champions League football, they still were not competing for players on the same level as the others which made up the traditional "top 4" as it were back then. Very recent history shows your argument is not valid. Other clubs have been a bigger attraction for years now.