Why does it do physical damage? Madreds Bloodrazor did magic damage. i would expect the same of BotRK seeing as it is its replacement. Armor is too easily built, so why would I buy an AD item that is simply going to be overly countered by the massive amount of armor when the new MR items aren't really any good unless you are a mage(except Maw)?

This is the age of armor penetration. It's fine.

Armour is less easily built these days and much easily countered.

I'm not seeing why this is a problem. Doing magic damage was Madred's Bloodrazor's problem.

You're mistaken. Bloodrazer wasn't to counter armor, it was to counter health stacking. If you want to counter armor, build a last whisper.
The reason bloodrazor was trash was a combination of its poor stats, ludicrous cost, and the fact that its passive health shred did magic damage, which AD carries (those who the item was presumably designed for use for) do not itemize to maximized.
BotRK brings a much better build path and the fact that it does physical damage enables Carries to continue to increase their overall damage output by utilizing armor penetration items, which ensure that the item is doing as close to its 4% health shred as possible.