I know nothing of BTE; I use drip lines under mulch for the reasons you state above. Overhead irrigation and moderate rain are blocked by thick mulches.

Over time the drip lines can get buried too much (as the chips decompose), so it is a good idea to lift them occasionally if you don't want them to dissappear under roots etc.

Compacted mulch should be fluffed up with a rake occasionally.

The care-free garden is a myth...

I have great success with thick mulch layers but you need to irrigate during the summer to keep everything from going hydrophobic. It'll rewet with enough rain though.

I'm a big fan of MP Rotators. They are a low precipitation rate emitters originally designed for hillsides to prevent runoff.

Thick mulching is wonderful. My water use is much less. I rake back the chips and lay down trimmings, leaves, scraps. In 6 months, it's gone and I need to get more mulch. It goes down faster than my compost pile does.

I purchased a very finely-ground mulch that held moisture nicely, but once it dried, it became impenetrable by water.

Fluff with rake to improve permeability.

Water eventually moves down from mulch into soil (gravity!), but it takes a while. If it is hot and dry it can evaporate before it moves down.

Maybe the wood chips you used were too finely chipped and compact. Larger wood chips let water flow through easily.