I think the main problem is: vias could occupy significant space from other components, thus a larger board is necessary.
On the first picture a TH vias allow us only four pads to be placed. But with a blind via or without a via we have place for six (or more if we have more rows) pads. A larger BGA component could be placed here this way. source
And at the end reduced size means reduced cost.
But to defend the vias a little:
There are cases when they are useful. For example at high power dissipation componenets thermal vias could be used to help dissipate the heat by leading it to large copper-pours.
All in all it is very application-specific and could have both advantages and disadvantages as well. It is up to you to find the balance.
Best Answer
Yes, you should remove it in most cases, because it can act as an antenna or cause other problems.
You can do this in Altium by selecting the 'remove dead copper' check box.