I dunno. I think it's somewhat counter-intuitive that they're more dangerous when grappling then when eg throwing rocks or shooting arrows or stabbing with spears.
This is exactly the problem. 1e has a lot of these problems though. Basically every time they attempted to make rules for adjudicating something new they created an entirely new subsystem. At best these subsystems are not coherent, they produce results which are all over the map.
1e has actually got quite a few 'combat systems'.
1. The core melee/missile combat system.
2. Spells (at least integrated fairly thoroughly with the rest, but still the rules for when a spell goes off and if it is interrupted by an attack are pretty wonky).
3. Psionic combat - works on a completely different system of segments, has radically different power levels than melee/spells. Very problematic, at best. Basically won't integrate with the rest of 1e without causing huge changes in how the game works.
4. non-lethal combat (DMG style)
5. Unarmed combat, DMG style (pummel/grapple/overbear).
6. non-lethal combat vs dragons (MM)
7. non-lethal combat (UA Appendix R)
8. Unarmed combat Style 1 (UA Appendix Q)
9. Unarmed combat Style 2 (UA Appendix Q)
10. OA Unarmed combat
11. OA Martial Arts
12. Dragon Martial Arts (3 versions, build on the OA ones)
There are probably MORE than this, but none of them really works well except when used by both opponents. Some of them can sort of mix, OA martial arts are about 2-4x more deadly than normal melee (depends on exactly what styles exist and how the rules are interpreted since they are quite badly written).
Anyway, the safest assumption is they should all be dropped except basic DMG combat, and maybe some judicious use of OA MA if you need, but probably best to limit it to OA games with only OA classes (IE the Samurai is tough enough to fight in this environment, although other OA classes aren't really).