When it comes to intra-EU, i am afraid that the whole LH group fares in Economy (due to the NDC capabilities (e.g. read here)) are usually a no-go since most of them are K or L and the "cheapest" awarding one is S but that is already a significant amount of money for a few miles (i think it's around 500 max.). Sometimes I find that SN which follows a bit different procedure than the rest of LH group might give you a S far for 100-something euro oneway. Premium fares are okay if you avoid the non-earning P one. You have to check these through the airline websites though (which is quite consistent at least) or Expedia and then you can try book through an OTA if there is a price difference (the risk of booking another fare is low).

For transatlantic to USA I used to pick UA or AC since their cheapest fares (in K) always award 50% accrual. Premium fares on TP also award a fare amount of miles but their economy fare categories are messed up (we discussed this in this forum extensively).

Asia is also similar with SQ or TG also awarding 0 miles in the cheaper fares.

You are not alone in feeling that this is annoying. Since you are based in Europe, you might consider your allegiance to *A (and A3) depending on your travel patterns and alternatives. Personally since I moved to Europe I switched to AF/KL where there is a difference in the tier/award miles scheme but at least you know that all fares (with few exceptions) will give you XP (the equivalent of tier miles). The cherry on top for me was when A3 introduced fees for upfront seating for gold members, so now I only fly them as needed (mostly trips to Greece) and avoid other *A airlines.