Thank you all for the valuable information. To answer some of your remarks:
It’s interesting that you called out Expedia by name, they absolutely do show you the booking class.
Expedia indeed shows the booking class, I was confused with other similar websites - I use plenty of them to find the best flights. I'll edit my initial post.
Still I'm not sure it shows the right information.
Next, Lufthansa (and its cadre of carriers) are notorious for these fares. Lufthansa K is the easiest economy fare to get from them and it earns 0% to almost every program in star alliance. I say K because it’s the one I know for sure, but K is gonna be paired with a bunch of those other codes as well.
As far as the P fare, that credits to a few but presumably that’s “deeply discounted business”. So it’s not gonna credit to most.
Now, as far as how to see the booking class on LH and how to change it to a higher one, I don’t know, I rarely use their website. Best guess is you can buy up a bit but you’d have to find it.
I tried to use Expedia to book a Brussels flight (I think Brussels belongs to the Lufthansa group?). All Economy options were shown as K, and all Business options were shown as P. Even the ones priced way too high.
Fly Aegean as much as you can and if you EVER take a trip to the US/Canada/Asia avoid the LH group.
I'll keep that in mind if I ever fly extra-schengen. But this is very surprising and disappointing. Is the LH group not selling qualifying ticket classes even for the expensive intercontinental flights?
if you only fly intra-Europe, then you might wanna just adopt one of the LH group mileage programs.
In the case of Lufthansa Group, the likelihood is that they are not paying Aegean any money (or at least a vastly reduced amount) if you take a flight in a non-earning fare bucket - and therefore there is no margin left for Aegean to give you any miles in return.
So my two options is either to go full Lufthansa, or forget about Star Alliance and start booking all the low-fare companies that are available. I'll definitely save a lot of money like that, but lose the frequently flyer benefits.
It sounds to me like LH Group is being anti-competitive to the Star Alliance partner carriers.
It would make sense for Star Alliance to enforce rules on this.