A good airline can train you regardless of your jet or TP time. I find all these artificial obstacles irritating. Having flown everything from a twin otter to a 747. I discovered a good aviator will meet the challenge. I suppose it's the difficulty in proving that you can do it before your hired. No company wants to waste $$.
That said, I was told the tail dragger was to hard, then it was the Beach -18 was to tricky then it was watch out for the TP and again the jet gotchas. Never had a problem and I just applied myself to each challenge. So far after 24 years not a issue. I believe the true skill involves being a aviator and not a shiny jet pursuer. It's unfortunate that the hiring boards lack the judgement to see the difference.
My advice, do what works for you and climb the latter. Each step is a notch in your experience belt. Sometimes you don't appreciate or are frustrated by your step. But believe me it makes for a more fulfilling career.