This idea comes up every time there is an increase in fuel costs. The problem is just putting in the cost index doesn't give you the best TOD. Without accurate lower level winds it all become a bit of a guess. The advantage of using a speed higher than optimum is that the fuel miles incurred at higher level are better than the same expended at low level.
Experience in the past has shown that if you set off with a slightly higher speed you can come back towards optimum to maintain idle thrust if the winds or ATC routing bring the aircraft below the optimum.
The whole process disappears out of the window when ATC say "Take up the hold".
The idea is one beloved of accountants who know the cost of everything but the value of nothing.

Tfly and Easy are using CI which produce descent speeds just above 250 kts, the only problem with this is that other airlines are using faster speeds. There is no doubt that these lower CI are to save fuel and it is a significant amout. As has been said elsewhere TFly and Easy are setting the lead here and as time passes the old higher speeds will become less common. At the moment when ATC control decsent speeds they are generally around 290-300 kts, ie 300 or greater or 290kts or less, the reason for this is because this is the percieved optimum speed. However as more opperators work on fuel saving maybe 260kts will be percieved as the optimum speed by ATC. I predict that the UK ATC enviroment will catch on to this first.
To those who say this has been done before (low cost index ) I agree it has, but in the past it has just been for fuel cost, now as well as that there is the desire to reduce carbon emmisions, which will be more powerful.

Just to throw one red herring back in to the sea ..... filed TAS is irrelevant as it refers to cruising TAS, climbing and descending aircraft are likely to be flying something slightly different.

As a controller, both TMA and at nose bleed levels, here's what goes through my brain cells:

First off, where are the inbound aircraft in relation to each other ?

If someone is 10+ miles ahead or on his own, then there's no need for ATC intervention. I'll monitor.

If there's 2 or more between say around 8-10 miles apart, then I'll use experience to judge whether speed control is needed or not. I'll look at aircraft types and use a bit of that experience to assess if I need speed control or not. If I do, then I'll want the guy ahead to be faster and the one(s) behind to be equal or slower. If I'm not sure, or can't provide constant monitoring, then I'll tell you the speeds to fly.

Under that, I'll be setting the speeds or providing vectors or vertical separation.

Additionally, if someone at the front can't fly fast, then I'll assess how far to go and what class of aircraft are involved and come up with a plan (turboprops CAN fly relatively high speed close in, so if less than 60 miles from the field, the jet ain't gonna win, sorry folks). That might mean the slow aircraft being vectored outside the sequence to let the fast ones in, all in the name of expedition.

There are no hard and fast rules, other than ATC wanting to have a nice easy plan which satisfys safety and then expedition.