If you actually know how D&D DMs design encounters, as I've stated twice in this post, balancing to 4 or 6 people is actually easy. Each monster on the Monsters Manual has something called CR - CR tells you the upper maximum difficulty of the monster, for example the famous Illithid Mind Flayer Arcanist has a CR of 8, meaning a party of 4 players lvl 6 could take 1 on with hard difficulty while a party of 6 lvl 6 could take it easy.
CR is a stat given to monster to balance them throughout the levels of the game as well, so goblins being CR 1/4 are usual enemies on lower levels while Giants vary from CR 5-13 and most Devils are CR8. Of course translating CR to a game will not be 1:1 but balancing encounter for a 6 party is not just upping HP/DMG/Number of Enemies.
Actually balancing for a 6 man party introduce more possibilities that, on Epic encounter like a Lich instead of only having the Lich they can actually summon a Beholder and the party can deal with it, making those unique encounter so much more memorable than just killing 1 powerful enemy.
But how can I add more monsters and difficulty? Late game Monsters are great enemies, most of them have really great stats, are immune to lots of stuff, have unique abilities and acess to spells as well as our characters.
Now IF I'm restricted to the 4 model party (Melee/Tank, Healer, Magic User, Rogue) I can't balance the combat well enough. IF I'm allowed to have 2 more spots I can add so much more to those encounters, I can have another Caster Character focusing entirely on Contolling and Dispelling and the Cleric can go smash and not have to focus on being only healer so it won't have to use most of it's action/bonus action healing.
By the way, most buffs are Concentration based, if you're so limited with a 4 man party probably you won't be able to get much more than a Haste and a Bless in fight since you can only hold one Concentration Spell, meaning our buffs are really limited like this.