I know I'm going to hit a nerve with you Ano, but coming from a background of installing systems for the last 20 years and working on equipment that dates back to the 60's or earlier, I'll state the fact that cross zoning is a band aid for poor system design, execution, maintenance or poor property upkeep. It always was and always will be.
The intent and purpose of cross zone implementation, historically speaking, was to get installers to move away from the practices of installing multiple detectors in parallel within a single protected space (environmental or cable faults typically the root cause) on the same zone or installing capacitors on the protective zones (those were fun) and allow a little more information as far as what is reported to the CS/event log as to which detector(s) caused the alarm to trip as the first zone in the cross zone is what is reported and if no further trips, that is given a RC of trouble, not alarm. Cross zoning would be used if you had 2 detectors literally in the same room/protected area or a door contact on an ill-fitting door with a PIR literally covering the same space. The door may fault, but the PIR verifies that no entry occurred, but the door contact could also be adjusted if the panel allows debounce settings, which is entirely different than zone response times.
In your specific case/example, you provided an exploitable fault of your system's design/programming. I would be able trip a motion within your house, which would (assuming you have CS monitoring) only generate a trouble and wait a second over 3 minutes and trip the next detector and every CS report will only be a CID trouble, which depending on their protocol, they may or may not dispatch or defer reporting to the end user as troubles, especially non-fire related, are lower on a CS priority list. Enough trouble conditions being reported, it's possible that someone could even cause your panel to initiate a swinger shutdown and then negate any further dialer reports, either via the single zone or by trouble conditions in their entirety (CP-01 and false alarm reduction programming). Also, depending on the panel itself, the siren may or may not sound upon generation of the initial cross zone fault, many do not actually sound the siren as they are "waiting" for the cross zone pool to generate the actual alarm.
Cross zoning existed for at least a decade before the CP-01 mandate, which in itself only forced some hard coding of default values on certain data fields so installers were forced to either modify the values to what they typically would have used (remove/disable items like bell timeout, dialer delays, exit error reporting, cancel reports, etc.) or leave as default. For the most part, outside of some installing dealers making poor programming choices (extremely short entrance delays, no secondary E/E delay point when garage attached to house, etx.) The main relationship of CP-01 and it's voluntary implementation by the manufacturers was due to an increasing end user false alarm generation rate, all of which led to many municipalities requiring verified response (AAV, CCTV or even ECV) including no response/private patrol response only and further tightening of municipal alarm permitting policies and the levying false alarm fines and policies. The main intent was to have a party responsible for the proper installation and maintenance of all of these systems, which unfortunately, the mass market installation/monitoring companies and DIY have put a black eye on the industry as a whole due to simple misunderstandings or poor training on the product with both parties being guilty of it (pros and DIY alike).