1. The goal isn't to get the highest promotions, it's for units that are good overall.
2.amphib is a good promotion that can save turns in a war and save units, although I do admit I don't use it nearly enough. Yes you only need one medic, but that doesn't make medic not a valid discussion in CR vs combat, and you don't want to give it drill, as it would be chosen to defend even at much worse odds compared to other units. Shock may become useless at gunpowder but is useful the game before that, same with cover. Charge is rare but can be useful. I don't believe you said anything about formation, the AI loves mounted, so its good. Combat hits everyone too, and in more situations, with very similar odds.
3.Good point, but wouldn't you want to destroy the Stack so you can benefit with the extra GG points? Those extra points plus the better combat promoted troops out of it is a lot better than using defenders.
4. I'm more of a run pacifism get a lot of GP player instead of war in Medieval, as I hate castles, so I don't have the units to use the money to upgrade ground troops, I have to build a lot of trebs and upgrade them, then using the draft to get out a good chunk of my ground troops. I'd rather take my time running those mines optimally most of the time as cottages are worse than them. I'm not too good at it yet though
I don't support the Schutzstaffel
1. No, amphib is not a good promotion, even when it comes for free (marines), you get better odds with CRIII troops (tanks). When it doesn't, three promos are much better spent on CRIII. CRIII is 85% mods (+10% vs gunpoweder defenders is going to be extremely likely if you are skipping a mace/treb war), CII/Amphib is +20% for combat and perhaps +50, which is less than than CRIII outright and if top defender is a gunpowder unit (pretty much always the case from rifling to the end of the game barring a brief lull between RR and AL) it is exceedingly rare for amphib to come out ahead
even when both units attack from a naval vessel. CRI is not that hot true, but CRII and certainly CRIII are extremely powerful; for three promos I just don't see how you can mathematically expect to get more from CII/Amphib than from CRIII; perhaps you are thinking about amphib elephants
Medic is a worthless arguement, unless you intend to eventually make an ubermash (WIII/MIII; in which case an ancient medic needs to be melee in order to get W promos) you make a chariot in the ancient era and either win enough fights for CI/MI or get it straight from a rax/stable/theo/vassal/settled GG as generally you want your medic to be more mobile; in either case it is one freaking unit and is less than 5% of your promo choices it is indeed irrelevant. When you have a choice, put drill on a musket, he can get medic and quickly fall behind the rifles, grenadiers, and MGs. 9.9 is going to get picked more often than 9 with a first strike.
Formation is a garbage arguement. At most you should need 1 unit in 10 to be formation (and at pike that should drop down to 1 in 20). At the time frame where mounted require the most stack protecters (axe rush) you don't have three promos so it is moot. In general stack protectors are a red herring. Efficient play dictates that you have perhaps 4-8 counter units (total) getting shock/formation/pinch. In the case of formation, it is exceedingly better to go drill; the big danger is getting hit with a bunch of suicide siege first; DII keeps them healthier and increases the odds that your defensive units will escape unscathed. If the enemy has enough mounted to be a nuisance, let them come into your territory and bang their heads against some well placed CG stacks.
In reality counter units are defensive units. They are an exceedingly small portion of the stack. You should promote them first and ignore them, using them to kill redlined and outdated units after your main combatant troops mop up the strong defenders. In most wars the will fight only handful of times (<5% of your total battles) and as such are not a significant strategic concern. Your city attacking units, on the other hand) will fight multiple times (normally 1-2 times per city) and are where the bulk of your promotion decisions are made.
3. No. GG points is, at most, +25% to the troop strength (either via increased numbers or better promos out the door) from having one bonus GG to use. Moving on to the next AI, getting an additional turn to work my new land, etc. is much more important. Hitting a second AI with a tech lead is FAR more important than getting more GG points. Further, the more you war the lower the return on GG points. Let's not even consider the risk that your AI will cap to some other AI and either spark an unwinnable war or deprive you of those key last 1-2 cities. The goal is land, not shiny troops and GGs. Shiny troops and ggs are useful ... to take land, nothing more.
4. So you are opting for a long term weaker economy in order to leverage a short term gain. Fine, run with it. That, however, is not optimizing long term payout; cottages pay more than mines if you do a full optimization (and for you a full optimization would screw the mines and opt for farms). Just remember that if you do choose to maximize tile yield, particularly long term per tile economic yield, cottages beat the utter crap out of mines.
The numbers don't lie. For the majority of your attacking troops CRII and CRIII are better than CII and CIII. As the game goes on, CR becomes stronger compared to combat; the units that get both become relatively weaker and for a while disappear. That is what you are seeing, not CR itself becoming weaker.