A couple of things on this (and perhaps unsurprisingly going to defend the Spell Identification rule)...
1. I know that not every table uses these, but my table has Spell Cards... So, when a Spell-caster declares that they are casting a Spell, they simply place the Spell Card face-down in front of them... There simply isn't any non-sense of people cheating & deciding which Spell they were "really" casting after they find out if it's Counterspelled...
Well, except for spells that say, "At Higher Levels". It's still easy enough to force a die roll.
2. Spell-casting is not a uniform science where a given spell is cast in identical ways regardless of who or what is casting the spell... Certainly there could be some overlapping Verbal or Somatic elements, if there is a common instructor, but even then there is no guarantee... The need for every Wizard to inscribe their own spells in their own spellbooks, in order to memorize a given spell, indicates that each Wizard's spells are uniquely developed methods of reaching a more universally understood spell effect like "Fireball"...
This is why a Wizard can add new spells to their spellbook that they didn't learn from anyone else... because the Wizard developed a unique way to cast a spell that can also be cast by other Wizards (or Sorcerors, Clerics, Warlocks, etc.).
3. The Spell Identification rule also highlights the importance of a Familiar. A Familiar acts independently, and can communicate Telepathically with it's Summoner when it is within 100ft. This means Spell-casters with a Familiar have an important advantage when using Counterspell, versus Spell-casters without one. The Familiar can use its Reaction to identify the Spell & Telepathically communicate the Identification, at which point the Spell-caster can decide if it's a Spell that's worth Counterspelling...
The problem I have here is that #2 and #3 work against each other.
#2 is a narrative explanation. That's fine. I prefer narrative explanations! However, the reasoning here doesn't work with the mechanics of a spotter.
Imagine this. You're playing a game where a machine drops a meter stick. Your job is to catch the meter stick as quickly as possible. The shorter the distance the meter stick has fallen, the higher your score. You may have played this game in grade school as a reflex test. Now imagine we change the game. The second game is just like the first, except you're wearing a blindfold. Additionally, a partner next to you can tell you when to catch the ruler. Which game do you think you'd do better at? You're now reacting to your partner's reaction instead of the ruler dropping, and your partner is reacting to the ruler dropping. It's
not possible to be faster at the second game.
So, if #2 is correct that it would take too much time to see a spell, identify it, and cast
counterspell by yourself, then by that reasoning #3 also doesn't work because it
must take more time to react to another person and cast
counterspell when that person had to react to the spell, identify it, and shout out what it was.
#3 also doesn't work, but that's primarily because a familiar isn't going to be able to identify a spell. A Cat is about as intelligent a familiar as you can get, and they have Int
3. Making a DC 15 Arcana (Intelligence) check when your roll is d20 - 4 (Int) + 0 (non-proficient) is pretty unlikely.