I think that's the slight problem bass players have compared to guitarists. - I think there is often a lot more colouration given by effects, amp and speaker, A patch set up to make you sound like John Squire of the Stone Roses for example, will probably get you in the ball park given similar pickup types.... with bass it seems a bit more subtle and playing with small margins, I'm pretty sure to get a specific tone that will work for a wide range of basses you would have to kill a lot of the dynamics.
And yes, not enough clean amps. I liked the SWR and EBS sims Zoom have. Going back to John's Dr Tone stuff one thing I took from his latest flat mids amp settings is how low he ends up running the gain on most the models to get a clean sound.
Also the fender bassman amp sounds nice clean.