I understand your argument, But I added the reason why I would pick Frozen Mallet. With the 1 point in utility and such your red buff isn't going to last forever. especially if the enemy also have a jungler. I'm not saying Frozen Mallet Is the best weapon, but its useful in every 1v1 scenario

IMHO, you don't need frozen mallet, if you are going for jungler, because you will have redbuff, not to mention all your skills either disable, make you faster or give you any other chasing benefit, so slow isn't a must. I'd probably go thornmail or warmogs, or something that gives both armor and HP. If you already went for starks, maybe you could also transition into a support hero if you don't need to jungle and carry, maybe aegis of the legion or Randuin's Omen, Also, I'm pretty sure Rylai's would be dope with the bringer skill :) but i need to test that... also only 500 hp bonus so it doesn't help that much...

If you still want to support you can either take S.Shroud or just go for warmog for maximum hp.

This build seems to be very squishy. I understand you have a Bloodrazor and Frozen Mallet for some HP and Armor and of course lifesteal to keep you alive.

But I feel you could change the Bloodrazor or Bloodthirster for something like a Guardians Angel or Banshee's vail.

But other than that I think it's pretty good.