why balanced power last before component?

Some noise does pass between the primary/secondary of a balaced isolation transformer, especially toroid, which just about all the popular units employ. IMO, its more effective to place the other device before the balanced power unit, to act as a pre-filter.

It's quite possible that the filter does not want any potential to ground on the "neutral".

Well, the power device 'after' the balanced may not be designed to handle balanced power.
I definitely would NOT stick a balanced device before any power conditioner unless you wrote the factory and found out if it is good to use with balanced power. IE it works as well with it as not.
I know nearly any electronc component can work fine with balanced power. but the point of a conditioner is to 'adjust' the AC power. and it may have 'unbalanced' tweaking to the AC. which would be messed up with balanced AC coming into the power conditioner.
It all depends on the way the conditioner works.
So without an ok from the manufacturer of the PC, i would only stick a balanced transformer after any power conditioning device.

If you cannot get an answer, look inside the power conditioner. Does every part of the device act on both hot and common AC line equally? if YES, then the balanced AC would work, if no, then not.

I have two Furman balanced power conditioner-15 amp and 20 amp.

I have had no problems running Shunyata Hydra 2 and Hydra 8 after the Furman.

I had inquired of Shunyata about any harm that would happen if I ran two Hydras together -daisey chained-as Blue Circle used to do.

They said not to do it.
A year later they come out with a daisey chained power conditioner.

I was never curious enough to try the Hydra before the Furman.
Somehow it just didn't seem right.

The Furmans have a large transormer and to rob it of any juice, filtered or not, it just seemed wrong to power it thru a Hydra 2.

In my mind I felt delivering 20 amp dedicated line to the Furman was a good thing to do.Then when the power is balanced, filter the balanced power.

It would be informational to know if anyone has done as Elizabeth has suggested and what the outcome was.

All I can say is that no harm was done to any components doing it my way.