A sync is a copy with better manners
Every integration is the same shape underneath. System A holds a fact, system B needs it, so a job runs on a schedule and writes a copy. The copy is correct at the moment it is written and drifts from that moment on.
Mostly the drift is small enough not to matter. Then a customer changes their billing address, and it updates in one place, and an invoice goes to an office that closed last year. The integration did not fail. It did exactly what it was built to do, at the interval it was configured for.
The failures are not where you look for them
When people worry about integrations they worry about outages, and outages are the easy case: something breaks loudly and somebody fixes it.
The expensive failures are quiet. A field that stopped mapping after a schema change and now silently writes nothing. A record that failed validation on one side and exists on the other. A conflict resolved by last-write-wins, which is a decision nobody made about which system is authoritative — made a thousand times a day, at random.
Integration counts are a strange thing to advertise
The industry has settled on advertising integrations as a feature, and more as better. Four hundred integrations is presented as capability.
It is also four hundred sync jobs, four hundred field mappings and four hundred places where two systems can disagree. Nobody maintains four hundred of anything well. The number describes the size of the problem as accurately as it describes the size of the solution.
What we are actually arguing for
Not that integrations are bad. We have them, you will need them, and connecting to a bank or an email provider is obviously right — those are genuinely other people's systems.
The argument is narrower: your own customer should not be an integration. Sales, delivery, support and finance all needing the same customer record is not an integration problem, it is a design decision that was made badly earlier and is now being patched.
The test is simple. If a fact about your business has to be copied between systems you own to stay correct, you do not have an integration problem. You have two systems where one would do, and a scheduled job apologising for it.