I think the pressing itself works quite well, actually. But thanks to only having two defenders as coverage, they have an additional player to press so who knows how it would look in a "normal" formation. But in general, I think you can play a pressing system with Kane upfront. Not every player has to be a relentless workhorse against the ball, often it is enough when a few cover passing lanes intelligently.
One way or another, it is still early days with Kompany. Maybe the vulnerability comes from players not fully understanding his instructions yet, maybe it really is a tactical flaw that he could still correct, etc. I'd love to see him fail for obvious reasons but let's not jinx it