Why can’t we connect PS4 controller on ipad

You can if your iPad is updated to IOS13

Turn on Bluetooth in your settings then hold the PlayStation button on and share button at the same time on your controller. You'll see DualShock 4 Wireless Controller pop up in your Bluetooth list.

then connect by cable it to a computer with itunes installed and update it using itunes on the computer

Update your iPhone, iPad, or iPod touch - Apple Support