The more general the effects of multiclassing are, the easier it is to predict the trade-offs and design/build for them. A MC fighter/wizard in 2nd Edition was actually pretty good for the most part because the mechanics just split the XP in half and the way the XP tables scaled meant you were probably going to be 1-2 levels lower than a comparable single-classed character. A MC fighter/wizard in 3E with an even class/level split was much worse off because the traditional caster classes weren't trailing by 15-20%, but by 50%, which is why prestige classes like the Eldritch Knight and Mystic Thaumaturge were more-or-less required to be viable.
Personally, I don't think approaching it from the equipment angle works well. In part, this is because post-2nd Ed. AD&D's mechanics don't consistently present "heavy" weapons or "heavy" armor as fundamentally superior to their lighter counterparts. You could, but in so doing you are implicitly suggesting that using anything but the equipment in those categories is mechanically inferior. The lightly-armored swashbuckler in leather with a rapier becomes an entertaining concept/roleplaying choice, not something you can realistically keep pace with in combat because the system's mechanics make plate armor and a great sword better in most circumstances.
E.g. The Complete Fighter's Handbook for 2nd Ed. introduced the Swashbuckler kit. You specialized in stiletto, main-gauche, and rapier; got a whopping +2 bonus to AC when in light armor (i.e. leather or lighter) or no armor; and a bonus to interactions with the opposite sex. But ultimately you were a bad fighter, mechanically. +2 to AC could't make up for the fact that leather's base 8 is in competition with plate's base 3, field plate's base 2, and full plate's base 1. Being able to gain +1 to Parry with a basket hilt was in competition with a two-handed sword doing 1d10/3d6 damage. You could contrive situations where the heavily armored fighter with a massive weapon got into trouble, but it was just that: a contrivance.
Once you moved to 3E, heavy armor no longer had the sense of being strictly superior. It had inherent movement penalties, inherent max Dex bonuses, etc. If you had a high Dex and no arcane caster classes, going with chain shirt was the de facto good choice. If you had low Dex, heavy armor. And medium armor was pretty much ignored. You could say, "Ah, but isn't it good that light armor is now more viable for fighting classes?" Sure, but heavy armor proficiencies are things that cost resources and heavy armor is a thing that arcane casters have penalties to use, implying that there's something inherently valuable about them -- when in reality, most classes have one or two optimal types of armor they can wear based on their classes and stats (i.e. Strength and Dex).
In 4E, armor and weapon choices ossified even more. IME, if you were in hide armor at 6th level, you'd be in hide armor at 16th. You were just picking what type of hide armor you wanted to be in, which feels pretty boring, IMO.
All of this is to say that you can't really have these things both ways. Either certain classifications or armor and weapons are designed to be fundamentally better than others or they aren't. If they are, you can design MC mechanics around limiting access to them, but those categories are always the optimal categories and selecting anything else is inherently bad unless you're restricted. If the weapons and armor are designed to have situational or build-specific trade-offs and not to be inherently superior/inferior, limiting access to categories only works if the restrictions are extremely tight, i.e. more is excluded than included. Otherwise you just build for the equipment you can use, which is designed to be on-par with what you can't use, and you have access to enough choices to adapt to any situation you come across.