The point still stands that even with a ticket with no baggage allowance, some *A airlines will allow a free bag and others will not. Don't expect that they will.
For example, in 2023, an itinerary on one ticket, AC standard reward on the following metal AC-OZ-(stop)-OZ-(stop)-NH-TG-SQ-(stop)-SQ-(stop)-AC had bags checked in with:
1. AC - fee waived via AC status/credit card
2. OZ - no fee charged, checked in with agent
3. NH - no fee charged, checked in with agent
4. SQ - cannot pre-pay online, airport self-check-in errored out, they wanted $15 USD/kg ($345 USD for 23 kg) but willing to settle at $200 USD/bag for US/Canada rates. Disputed after trip to $75 CAD after trip as per AC ticket details.
5. AC - fee waived via AC status/credit card
If you want bags to be included when checking in on partner metal, ensure you select a reward that includes it.