I have been through a similar situation. Moved to Canada from the US while having 30 or so cards. I changed the address to that of a friend who will get the occasional mail but all correspondence is generally electronic.

After about a year, most of the cards with annual fees I closed because they were not worth it anymore (few exceptions like Citi Prestige and Chase IHG which I still find valuable and Amex SPG because I got a good retention offer). The cards without annual fees I planned to keep to maintain my history. Eventually I ended up closing some of the no annual fee cards too just because I couldn't be bothered to keep track of them all. I do maintain at least one no fee card from each of the major issuers to keep the relationship in good standing.

I don't use the US cards for daily spend in Canada because I don't have enough $USD to keep paying them off indefinitely and it is not worth it to keep converting currency. Also the risk of a shut down if I keep using them in Canada.

I have a Canadian Amex SPG that I use for my daily spend here and am quite happy with it. I will occasionally buy a $1 Amazon reload with my US cards to keep them active and prevent the account from being closed. Not to mention using them if traveling to the US.

This hasn't prevented me from getting new cards either. I recently churned 2 Citi AA Plats and manufactured the spend with NW Buxx (now closed) without ever having the card in my possession. Pure online methods of MS are very rare so now I only focus on cards with very low minimum spends. The only upside is that I will eventually get under 5/24 which would have never happened without moving to Canada .

Pro tip: cards from Discover, US Bank, Wells Fargo, Barclays and some smaller issuers will waive small balances of ~$1 (exact values differ for each of them). I buy Amazon reloads from each of these cards every month and earn about $70-80 in gift cards every year.