A 3000+g tank item will most likely not have the effect that you desire
A tank item that will scale well into the late game would be nice to counter to late game scaling ADCs and late game scaling damage champions, but the issue is that tanks are generally low on gold in the game.
Especially in LCS but less so in normal ranked games carry champions with high amounts of damage are getting the most CS, the most kills, and the most gold. Damage leads to more gold, because with more damage, you can CS easier and last hit enemy chamions easier. That means that stacking to 3k+g on 
etc. will be harder than
etc.
Basically, since a late game or snowball champion gets more gold, expensive items that are 3k gold or more will be easier to get for them than say a
.
For example,
is buffed into a late game item that costs 3.6k gold, and gives 40 extra armor(or something) while retaining its other stats and passives. Since that item is so gold efficient, yet so expensive, that it will be easier for a
to pick up than a
.
Let's say caitlin is facing a team that has
and
. Randuins is impossible to pass up in this situation, and also it has more stats. Now there is a 182 armor 2734 health(well technically 2384 but with a BT shield) caitlin with crit damage reduction and a slow.
Meanwhile the allied braum is still sitting on just under 2k extra gold, still 1.6 away from the raunduins.