Do card bonuses lead to increased discretionary spending compared to more basic cards?
In general, yes. Here's a study that proves most people do spend more. (Download the entire study here.)
However, it highly depends on the card owner's personality. As someone who has migrated from cash only, to cards with no benefits, to cards with points and/or cash back, I can tell you from personal experience that as soon as I transitioned from cards with no benefits to cards with points and/or cash back, the amount that I spent on the card went way up. However, the total amount of money that I spent generally did not change. The reason is, as soon as I switched to a CC with benefits, I had incentive to stop using cash and start using the card, for nearly everything I purchased that would accept a card. After a while I stopped carrying cash except $20 for emergencies. Furthermore, when I went out to lunch with my friends or coworkers, I would always be paying with card, so I'd always offer to pay for the whole check and they'd just give me cash to cover their meal. Note this comparison is only between cards without benefits and cards with benefits. My personality is not such that I would ever purposely spend more to get 2% (or more) back. I think of the cash back as a discount. The only exception to this (that I can think of) is I once had a travel points CC and I was very close to getting 2 free plane tickets to Hawaii when I was about to travel there, so I used my CC to buy some Amazon gift cards to put me over the edge. (But I didn't splurge on the Amazon cards- they lasted about 6 months before I used them up.)
Now, comparing a CC in general to cash only makes a much bigger difference, primarily because it enables you to purchase things you normally wouldn't have enough cash for. This includes me too, since although there were times before I used a CC that I would go to a bank or ATM to get more cash and then return to the store, the hassle typically wasn't worth it except for very specific items. The problem many people run into here is that not only do they not have the cash on them, they oftentimes don't have the money in their bank account either, and that's when the trouble begins.
Do people spend more when using a card that comes with (cashback) bonuses, compared to using a card that doesn't? Intuitively, I would think yes, or credit card companies wouldn't offer those bonuses;
In general, banks make money on every purchase you make (usually somewhere in the 2.5-4% range), so offering perks is a way to gain new customers (competition with other cards) and help retain them (with unspent points/cash). The value of new customers is extremely high considering every customer is either barely profitable, or extremely profitable if they ever pay interest, draw cash, have a late payment, or extend their banking relationship further with the bank.
Side note: none of my credit cards, even those with 2% cash back on all purchases, have any annual fee.