We had a large discussion here on the Regimental System not long ago.
There is really no reason to get rid of it, but there is just as little reason to keep it either.
The comment about not being able to have pride in a numbered unit is absolutely false. My regiment did not mobilize for World War One; it contributed troops to a numbered battalion of the CEF, the Tenth. The Tenth drew troops from the 103rd Calgary Rifles and the 106th Winnipeg Light Infantry.
Guess what - it didn‘t bring ANY of these regimental traditions with them - no black buttons, no buglehorns, just a numbered battalion. Well guess what again - they were cited several times as being one of the best units in the 1st Division; Currie himself noted that of all the units he had personal experience with, the Tenth was the best at reorganizing after a show and being ready for the next one. The battalion won two VCs and kept an Association going strong into the 1990s when the last Tenth Battalion vet passed away. The association bought itself a new Colour - after the war - and lobbied to get Kitcheners‘ Wood as a battle honour for the 10th. These guys had pride! Their nickname was never anything more than THE FIGHTING TENTH.
The CEF as a whole consisisted of "numbered units", some of which drew traditions from Canadian regiments - but most did not. They simply created their own. "Tobin‘s Tigers", "Lethbridge Highlanders", etc.
You could rename PPCLI as 2nd Canadian Infantry Regiment and men would still feel the same amount of pride, because that comes from training, comradeship, achievement, and other factors external to the regiment.
Don‘t get me wrong - you would definitely have lost some things, but operational effectiveness wouldn‘t be one of them. You would have morale problems for those already in, and I do believe recruiting. I think bossi talked about the recruiting value of a Highland regiment, and he‘s right - it is also of use to let you join the same regiment your father served in, or grandfather.
But you also would have NOTHING to gain by dropping the regimental system either. I am in favour of keeping it, but I want to point out that many armies do have pride in their numbered units, and have fought very well with them. The Wehrmacht got rid of regimental distinctions in the 1930s ("1st Saxon Regiment", "2nd Bavarian") and though they did have regional affiliations for their regiments, and reflected this in the divisional titles (which we rarely see reference to in English), the only real distinction they used to differentiate in the majority of cases was a number on the shoulder strap - which was deleted after the outbreak of war in 1939 as a security measure.
Those same traditionless regiments took over all of Europe and fought a skilled defence of it when they started losing.