I'm guessing you have it all back together now, but I installed a Melling kit with cast iron ratcheting tensioners and a high volume pump. kit did not come with phasers, those are still original. I would definitely put a high volume pump in there if its still open.
Some people definitely do, but what they don't realize is that oil is bleeding out of the tensioner due to a blown seal and that's causing low oil pressure at the cam shaft. That low pressure can cause accelerated wear, and the head has no cam shaft bearings, it rides directly on the aluminum head. So if it gets too bad you are out a cam and cylinder head. . . This combined with the already low oil pressure the 5.4 has at idle (so much so Ford turned the gauge into an idot light because too many complaints) its really a recipe for disaster.