Luckily, since my 11th birthday, I'd replay and re-strategize, re-build my party. (often w/ a Magmar/Electabuzz.) One thing never escapes me, how laughably fortunate I was to stroll right through from Pallet to the Champion seat w/ only using Bulbasaur. How I managed to beat Charizard w/ Venusaur was beyond me, must've been over-levelled, poor opponents. (Wait, I must've beat both Gengars AND Dragonite w/ Venusaur as well. Wow, WAY too lucky.)
Whatever the game, the atmosphere replays itself upon the very first entry. (I was incredibly wide-eyed approaching S/M's League.) W/ Venusaur in hand, I must've glanced at that building forever, it seemed like minutes before I would collect my composure and readily stock up on items. "Is Venusaur gonna lose? E4, huh? I gotta fight four people?" Not even occurring to me that dear ol' Blue was gonna jump me after I'd FINALLY beat Lance.
I remember the shattering of my excitement. "You are finally the Champion, or at least, you would have been..." Lance wanted to mess with your head a bit, before revealing a big surprise, (Only applies to those playing for the first time. After the thousandth, I only feign surprise.) being the only person to make it past the then-Champion Lance would be your rival. (Also, to date, being the only rival to ever make it to Champion seat.)
With Ice Beam, the E4 are simply old rivals there to test my strength and patience on. And farming. Mad farming. You can't get more exp than E4.