If there’s consensus to use numbering of daily sections or stages then I would prefer new numbering for every branch. Have a look at EV17 - would you divide the ViaRhôna part into the same number of stages as the R1 part from Andermatt to Genéve? I wouldn’t do that.
About discouraging branches, what about doing EV15 next? 
There are two branches from Lake Constance to Basel right and left of the Rhine, only one in the city of Basel, two branches right and left of the rhine from Basel just to the border of the Netherlands. The branch on the right side of the Rhine is sometimes interrupted and seems to end a bit unmotivated (or just not developed) at Spijk.
If we number daily sections and do a renumbering for segments, I would prefer only to restart the numbering at borders if there is the begin/end of a segment. I would not restart the numbering of the east segment between Basel and Karlsruhe at the French-German border near Neuburg am Rhein.
And I’m not in favour of creating disconnected relations per country, if a EV route has multiple parts in one country. EV 5 for example with two or three parts in France: from Calais to Leers and from Grosbliederstroff (Sarreguemines in the GPX files) to Huningue and in OSM there is a third part from Apach to Launstroff see Proposal: creation of a working group for a more coherent integration of EuroVelo routes on OSM - #43 by Vinzenz_Mai
On the other side is the crossing of borders often a good cause to split the EV route in segments.