Stop Rolling Initiative
Illuminated by torchlight, the party descends into the tomb, the smell of death heavy in the air. They crawl the winding halls, taking care to scan the floor, the wall, and the ceiling for traps and ambushes. A heavy wooden door blocks their path. The Warrior kicks it open and the Necromancer shouts, "You're too late!" The sound of metal and bone scraping against stone fills the chamber as numerous skeletal figures rise. . .and the game grinds to a halt as initiative is rolled.
There is no mechanic clunkier than rolling initiative and the more combat your game has the more unwieldy it will feel. Some games simplify this by rolling for sides instead of individual combat participants, but this flattens the number of tactical considerations in combat considerably. Some groups use apps to speed up the process but, if you are like me, you prefer not to use tech at the table as it tends to distract.
Don't Roll Initiative, Draw Initiative
If you want a lightning fast method for initiative playing cards are the answer. Playing cards have an immediate, obvious hierarchy that make generating an initiative order quick no matter how many participants are in a combat. The best part is: you almost certainly already own a deck of cards on hand.
Here's how it works: each player draws a number of cards equal to their character's Dexterity modifier, plus 1. If their modifier is positive, they choose the highest card. If their modifier is negative, they choose the lowest card. If their Dexterity modifier is 0, they are only dealt a single card and that is their initiative score.
Aces are the equivalent of a critical success. Jokers are the equivalent of a critical failure. You can balance the chances of critical by either removing 2 aces from the deck, or adding 2 extra jokers (I do this in my game).
Once every participant has their initiative card, line them up in order on the table and place whatever token or mini associated with them on top of it. Not only is this method fast, it's highly visual - everyone can clearly see the initiative order. It also makes tracking things easier in combat as you can place tokens, dice, and counters on each card to represent damage, effects, etc.
Too Fast, Too Furious
It's true, if a character has a Dexterity Mod of +2 or +3 they will seldom end up going last. However, you can modifier the number of cards players draw with things like advantage/disadvantage and penalties. Reduce the number of cards they draw or force them to take the lowest option as the situation calls for it.