I don't think my left/right hand coordination is very good. cuz when my fret hand moves really fast, I pick slow. I do a lot of hammer ons and pull offs that way. but when I do really fast tremelo picking (brushing my picking as fast as possible creating 16ths or even 32nd notes), my fretting hand moves slow. i've tried many ways to improve that coordination by doing the chromatic 1-2-3-4 and learning paul gilbert songs (he's one of my greatest influences). but i just can't seem to get it right! and really... is there such thing as tremelo picking? i find tremelo picking kind of cheating. cuz i've been wondering if it's every possible to practice clean and crisp alternate picking bya metronome, and practice so much that eventually my alternate picking speed becomes as fast as the random brush of tremelo picking, or even faster! also, i can't sweep pick at all! and a lot of fast players do sweep picking. but paul gilbert doesn't sweep pick either! he plays arppegios by skipping strings and picking notes that make up the arppegios!
so basically, i want to master alternate picking! cuz when i do tremelo pickings, i find it really hard to switch or skip strings, and with alternate picking, i can! so my question is, can my alternate picking speed go as fast as tremelo picking speeds, or should I still practice tremelo picking. and if i should still practice tremelo picking, how do i practice left/right hand coordination with such picking?