The fighting style with shields "Protection", the lore bard´s "Cutting words", the "Defensive duelist" feat, Battlemaster´s "Parry" and rogues "Uncanny dodge" of the PHB are also reactions.
And if they end up using Xanathar´s, an official extended-rules book of WOTC that it´s been for three years you can add the druid of spores halo & more spells like gift of gab, absorb elements, etc
For initial release only the Player's Handbook has been confirmed so it is irrelevant how long other source books have been around.
Good catch on the additional usages but as these are for non mage classes they are only competing with attack of opportunity which could be handled by the currently proposed system.
That would be true if D&D would not have a thing called "multiclassing", you know, something that allows you to be a mage with reaction spells but also a rogue with uncanny dodge, a fighting style, bard´s cutting words, battlemaster´s parry, etc... and AoO, something that any character could do.
(ED) "Defensive duelist" "Sentinel" "Shield Master" "War Caster" and "Mage slayer" are feats that use a reaction and any character could get them.
Even a single class fighter could have AoO, defensive duelist feat, Protection fighting style and parry battlemaster maneouver, all competing for a reaction.
All of the above is from the PHB, just to clarify.
Anyway, I respectfully disagree with your reductionist statement from above about the reaction mechanics, both in D&D and in BG3 and, even if they do not include the usual rules of the core extended rulebooks; the reactions are a core mechanic of D&D5e that in my experience is used extensively so IMHO any resource expended to make it work smoothly and following the 5e rules would be a time well spent.
