To back up this statement, I can use some numbers from the Caltrain (California, US) electrification project, where the existing commuter-heavy Peninsula corridor is being converted from diesel-electric to 25 kV overhead electric.
Caltrain quotes the cost of electrifying the line at USD 697 million. See http://www.caltrain.com/Assets/Caltrain+Modernization+Progra...
Caltrain quotes the length of electrified track as "51+ miles", which I'm going to treat as "51 miles". See http://www.caltrain.com/Assets/Caltrain+Modernization+Progra... pages 4 and 7. The length runs from San Francisco's station at 4th & King streets, down to San Jose Diridon station.
Those two numbers above give us a cost of USD 13 2/3 million dollars per mile. But, that's not fully accurate.
Most of Caltrain's right-of-way is double-track. There are three areas with four tracks (for fast trains to pass slow trains), one area with three tracks (near the Millbrae station), and three areas with more than four tracks (one is Caltrain's yard and shops, the second is the many platforms at San Jose, and the third is the many platforms & yard at San Francisco). See an old Caltrain timetable at https://web.archive.org/web/20110513180702/http://acm.jhu.ed...
Let's say that San Francisco is about one mile of eleven tracks (so, 11 track-miles), each of the three passing points is two miles of four tracks (so, 24 track-miles), Millbrae has a mile of three tracks (3 track-miles), and San Jose has around one mile of twelve tracks (so, 12 track-miles). That leaves around 46 miles left of the 51 original, which would be double-track, giving us 92 track-miles. So, that's 142 track-miles, giving us a cost of USD 4.91 million per track-mile.
Of course, costs may certainly be higher in the US, where electrification (especially for mainline heavy rail) does not happen much (if at all), but still, electrification of an existing line is not cheap. For Caltrain, it makes sense, because this is a heavily-trafficed line in an area with many polluting vehicles (automobiles) that also wants to have a 'green' sensibility, as well as wanting the reduced noise profile.
When you consider freight, there are other issues. For example, in the US, heavy freight traffic lines use gondolas that can support two containers, stacked one on top of the other. That means wires would have to be higher than they would otherwise, and I wonder how how well those extra-extended pantographs would work at higher speed.