Everyone should do what works best for him or her. Using multiple cards does take a little more thought and the small (for me) inconvenience of having more bills to pay off each month. It's a matter of individual judgement whether these cons are outweighed by the additional savings.
As a fairly straightforward example, I happen to have a card just like yours. If it were my only one, getting another with the same benefits would let me get 2% cashback instead of 0.5% on three different categories. Obviously I'd save more in total, with how much being dependent on my spending in the three categories I choose for the new card. And I'd have to make the subjective decision whether the estimated difference would be worth the additional thought and effort.
It's also worth noting that no-fee cards sometimes offer sign-up bonuses. Just this past week, I saw an in-store sign-up offer for PC Mastercards that included 30k points. There were some conditions attached, but they seemed pretty easy to meet. Those who qualify for the "World" card get 20 PC+ points per dollar spent at Loblaws, RCSS, No Frills et al, and also at SDM, plus 2 cents per litre of gas at Esso. With the "World Elite" card, it's 30 per $ plus 3 cents.
Fee cards are obviously more involved. They're not for everyone, but they can save some people more than no-fee ones. As a simplified example, if you were to pay an annual fee of $100 and get 4% back instead of 2% on purchases at major grocery and gas chains, the break-even on just those two categories would be $10,000 per year. If you spend more, you'd save more in the end by using the fee card. In practice, the B/E would probably be somewhat lower since the fee card is likely to have 1% cashback instead of 0.5% on your other purchases.
One thing to be aware of is that some premium cards with 3% and even 4% cashback rates on selected categories waive the fee for the first year. So, if you're able to cancel when the year is up (as you pointed out, it's critical to read the terms that apply to each card), you can, in effect, have a no-fee premium card for a year. Whether the additional savings in that time are worth the additional effort is a personal decision that involves subjective factors as well as dollars and cents, but in the latter area, having a card with a higher rate than your current one is clearly beneficial for that year.
I was a two credit card person for a long time, one MC and one Visa, both no-fee, with staggered billing dates so I could always use the one with the later payment due date. I also assumed fee cards weren't "worth it" for me because I didn't and still don't charge all that much. It turned out that by choosing a better informed approach that involves multiple cards, I save hundreds of dollars per year. Maybe some other forum members can benefit from better informing themselves too.