I put nearly 400k miles on my 2000 Yukon 5.3 2wd. Original motor, did replace the trans after 161k miles. For about the last 100k miles I had this same low oil pressure on startup issue. Wish I would've known it was such a simple fix. In the end, it had some other issues when I finally gave up on it -- likely a leaking head gasket, was getting coolant in the oil. And finally the radiator went, that's when I quit on it. I bought this one new with 6 miles on it and I put all the miles on it except maybe 50 or so when I had a DD drive me home a few times.
My second Yukon was a 2005 5.3 2wd. Bought it with 191k miles and ran it up almost to 300k. It too developed the low oil pressure on startup, probably around the same mileage as my first one - maybe 250-275k. Transmission went on it and I decided not to repair it. Still have it, going to look to sell it I guess.
I'm now on my third Yukon from this body style. A 2003 5.3 2wd. It's a 1-owner vehicle I got with about 150k miles. Original motor and trans, no issues. Oil pressure is strong. At least now I'll be aware that this is a cheap thing to look at if I ever experience the low pressure problem on this one.
Love these vehicles from the 00-06 era. Would drive one forever if I could. Also have a 2012 Tahoe 5.3 4wd. Got it with 77k miles and it's now at 180k. It's been a solid truck, but the seats are way uncomfortable to me, and I don't love the active fuel management. Other than that, no issues at all. Still runs like new like when I got it from the previous owner. Knock wood.