Hoses & Kitchen Sink Taps

I assume, and it is only assume, that the self cutting tap just pierces the pipe when you clamp it on your existing pipe, but probably a small hole rather than the full 12mm you are likely to get if you fitted a T instead.
That could reduce the flow enough to stop the pressure washer working correctly, a lot probably depends on how much pressure you are getting from the mains in the first place.

From the link @ricky101 put up.
Low water pressure
If your tap is experiencing low water pressure, it can affect your pressure washer’s effectiveness. Insufficient water pressure leads to reduced cleaning power, making it more difficult to remove stubborn dirt and grime effectively. Additionally, low water pressure can cause the pressure washer to continuously cycle on and off, which can strain the motor and reduce its overall lifespan.

 

Quite a number of years ago I used a self cutting tap, mainly due to access issues, The hole they cut is possibly about 6 mm also the bit they cut out is retained in the original 12 mm pipe.