Great and very detailed answer Overmod, thanks for taking the time.
The same logic applies to trailing axles as to any idler axles elsewhere in locomotive design. The lower percentage of adhesive weight not on drivers, the better your starting TE will be for a given cylinder size. The shorter (and cheaper) your engine will be to build, or contrariwise the bigger an engine you can have for a given turntable size. One less axle to maintain bearings on, machine tread profiles for, etc.
The trailing axle provides for the wider and lower grate, etc. as described. It also provides lateral stability, particularly after the revision of the Delta truck as described by Alfred Bruce. When the restoring force is applied as far back on the chassis as possible, it can stabilize the chassis measurably against the effect of surge and augment.
The trailing axle also measurably improves stability in reverse moves -- that is one reason why N&W Y-class engines, for example, were 2-8-8-2s rather than slightly longer-wheelbase 2-8-8-0s. Locomotives without trailing trucks must rely on the flanges and tread profiles of the rear driver pair to do the steering in reverse -- and they are probably NOT optimized a la Stroudley to perform that job with panache, if you get my drift...
Note that lack of a trailing axle was NOT a major impediment to relatively high speed -- the LS&MS 4-6-0s and Chapelon's 240Ps being all the demonstration anyone could wish for. It was the higher steam-generation capability without ruinous draft and coal-lifting intensities that made the larger firebox so mecessary for high speed at high load...
Meanwhile, the drawbar location relative to tender geometry is relatively troublesome with no trailing truck -- the front of the tender becomes the means -- usually a wretched means -- of steering the rear of the locomotive chassis. A cognate example is the stability of the original Woodard Super-Power locomotives, with the 'clever' articulated trailing truck that made the locomotive act like a 2-8-0 in yaw; not a particularly pleasant thing especially when compared to an 'ordinary' Delta-trucked Mike of equivalent size forward of the firebox.
The rather obvious 'solution' to the loss of TE with 'idler' axles is to motorize them. Hence all the flavors of booster -- successful and unsuccessful -- including the checkered career of motor-tender schemes. Note that Franklin high-speed boosters were relatively successful, but Bethlehem auxiliary engines FAR less so... and even a cursory look at the drawings and the technology will show you why. (It will also show you some reasons why the axles in 4-wheel trailing trucks aren't conjugated for boosting...)
Gresley had a brief booster fling (the story recounted, along with Sturrock's steam tenders, in Fryer's book on experiments in British steam). They did not catch on over there because the costs of licensing, building, and maintaining what is essentially an intermittently-powered axle exceeded the practical benefits, in Blighty at least, of what they provided (especially compared to less-intricate methods).
What else do you need?
RME
I've read that adding the trailing axle allows for a bigger firebox, but are there any disadvantages to adding a trailing axle behind the drivers? The Consolidation, for example, appears to have been popular among railroads even after the Mikado was introduced. Thus there must be some advantage (perhaps just cost) to leaving that trailing axle off.
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