(1) OW airlines very clearly had a policy - stated or otherwise - to accommodate passengers on multiple tickets in the event of IRROPS. Otherwise, it wouldn't have been necessary for them to state the the "disruptions policy" was changed as well.
(2) CX has now made it clear - see the chart linked to by moa999 above- that they will not provide assistance to flyers affected by flight disruptions traveling on multiple tickets. This is a major negative that most certainly reduces the value of the OW alliance to a typical customer. For example, if traveling around Asia, and my CX flight into HKG is delayed causing me to miss the AA HKG-DFW flight, I am now stranded in HKG with no alternative other than to buy a new ticket at the walk-up fare?? If that is the case, then why bother booking my intra-Asia flights on CX?
(3) The excerpt from the BA policy posted by moa999 specifically states that the "Most Generous Allowance rule for baggage" will no longer apply to multiple tickets.
It is very hard to see how anyone would not recognize these changes as being unfriendly to consumers. It is likewise hard for me to understand how OW airlines think that this will make anyone more likely to fly with them.
As a OW Emerald, the only two things that I place value on are (1) IRROPS handling and (2) lounge access. These changes make both of those less valuable since (1) they won't provide it anymore and (2) my time will be wasted chasing around airports rechecking my bags.