cjk wrote:The tuba gives pitch and perhaps tone to the tympani. or is it vice versa?

It's vice versa. In my humble opinion. There is no instrument on stage that can match the fullness of a timpani hit (or bass drum for that matter), because there is no instrument on stage that can articulate that strongly. We can't give "tone" to a timpani hit because we can't match it - there is a huge dropoff in sound when the timpani sound stops. So I think it has to be that the timpani gives force to other instruments' articulations (among other functions that it has).
cjk wrote:* Bottom voice of the trombones.
* a 4th or 5th horn.
* giving the bass section more volume.
* giving more pitch and tone to the tympani.
Basically "special effects for the other instruments".
I don't mean to sound like a broken record, but if these are the functions of the tuba (and, if you include tuba occasionally being a soloistic bass voice, they are), the above is a very good argument for using smaller equipment. The tuba is never "the bottom of the orchestra" all by itself. But, better, more experienced, and more respected players than me see a need for big equipment and use it to great effect. And given that modern trombone players play bass trombones as tenor trombones, maybe it's necessary. So. My opinion continues to be considered but humble.