How exactly would we do these tasks and view these statistics using shared orders?
Well... what you need to do it? You need to know whether vehicle X is assigned to route Y and you need to be able to find all vehicles assigned to route Z. So, the current "shared orders" have what it needs to create "routes".
Well, as for how I imagine it... how about this:
Every vehicle with shared orders having extra statistics, like "Shared orders with x vehicles" "Route profit last year" and "Route profit this year" and in the "goto" panel extra button, "Route" or "Shared orders" and here commands, sth. like "shut down route", "upgrade route to this engine" and for trains "set default route capacity (x wagons)" (which will apply for trains and buys/sells wagons of all other trains with shared orders, so that they have the same amount of wagons as selected vehicle).
If somebody manages to code in the "equal interval" feature into the game, I would make it default behavior for all vehicles with shared order (turned on/off in game settings menu)
note: I think it should be possible with the "shared orders". Now the goto list of all vehicles with shared routes can be altered, so it should be possible to issue "goto depot" command and "buy/sell engine/train/wagons" command to them. As for the statistics, it's just taking every vehicle's with same shared orders statistics and sum the numbers. Problem is how it should handle situation when you sell some vehicle(s) with shared orders or give it different orders