Rush isn’t the same as haste entirely because of the boardgame element at play. Haste (Rush) in MtG is closer to the effect that Dust Wailer has than to the effect that Saberspine does, and that’s fundamentally why Magic uses it primarily to build up the color Red. Which again, is the issue at play. Black and Green get Rush in Magic too, but far less than Red, and Blue and White only very rarely get Rush because the idea is to balance it on faction-based scarcity. Tiger, Elucidator and Revenant ALL break this because they can be repositioned, pumped, AND Duelyst works on an “attacker’s choice” system.
It’s also silly to compartmentalize it as “nerfing Rush”- because it’s taking the complex elements of Rush and making design space out of simpler keywords (which we already get in minions like Maw and Dancing Blades.) Rather, it’s restraining the number of Rush minions available based on which faction they belong to, simply because Rush minions that are placed can bridge almost the entire map to attack while wearing a pump- something that is powerful and unreasonable to balance outside of minions like Tusk Boar and Makantor Warbeast- where the opportunity cost of Rushing pumps is offset by mana/additional card cost, or the effect is redundant with the rest of the faction to an extent where it doesn’t violate anything.
Consider old Third Wish. A buff spell that powerful simply can’t exist for as long as Tiger does. Or Kara’s old BBS, or Argeon’s BBS on Tigers. That sort of ability isn’t able to exist on spells or minions without breaking the game, because Tigers will push it over the top. Abyssian mirrors devolve into Revenant gunslinging, and Magmar mirrors tend to turn into "run away until you get Elu+TWave. The very existance of the board complicates Rush severely- and forces card for health exchanges that result in overly anti-climactic games.
Gaze and Rush are sortof the posterboys for detrimental interaction right now. But in Magic, I always jump to Thoughtseize and Force of Will. Counters with insufficient mana costs, and hand disruption that gives the caster too many options ontop of the information allotted create a sort of resource exchange that make one player limp. Usually, the way interaction will be detrimental is due to a lack of opportunity cost per the effect (usually due to low mana costs, no mana costs, wording that is too loose, wording that doesn’t work as intended.) Another fantastic MtG example is Armageddon. A spell that destroys all lands, the primary economy of MtG, and so the players exchange resources, but the player with the cheapest spells, and the most nonlands on board almost automatically wins.