The Heart Break Kid couldn't beat Taker, Triple H couldn't beat Taker, Lesnar has already lost to Taker at Wrestlemania and CM Punk, the longest reigning champion of my era couldn't beat Taker.
I used to watch wrestling back in the early 2000's and I remember the first PPV match I got to watch was No Mercy 2003, where the main event was Brock Lesnar vs the Undertaker in a biker chain match, a theme taken straight from his biker persona back then. Lesnar won.
The year before, The Rock faced The Undertaker and Kurt Angle in a triple threat match and won the championship, only to lose it to Brock Lesnar a few months later, giving him the record for youngest WWE Champion in history (which was previously held by The Rock). That was right before The Rock retired, kind of a shitty way to go, huh? Sounds like a similar thing here.
Seems like beating Taker fits with his character to me, but I haven't watched wrestling since high school. Is he really considered a second-tier wrestler by today's standards? He used to be intimidating as fuck.