Any fluid, liquid or gas which is in laminar flow will have an almost static flow where it contacts the cooler tubes.Carbon deposits should normally be removed from the cooler by means of the exhaust gas flow. The fact that carbon is building up and not being able to be removed by the exhaust gas flow is suggesting that something else is preventing this. The only other substance that can get into this area is oil that has come into contact with the combustion process.
I agree that if lube oil is carried over it will make the problem worse but overall the cooler doesn’t have the additional capacity to allow for an acceptable interval between servicing. As with most things under the bonnet it’s a case of squeezing it in.
Different subject but the cause of many machinery issues these days; most design engineers I’ve worked with in recent years don’t have a clue about maintenance, that’s the downfall of hiring graduates and not promoting from the experienced workers.