Compound interest encourages longer-term investments.
Banks want to hang onto as much of your money for as long as they can. With simple interest, you get the exact same interest payout every day/month/year - it doesn't matter how long the money has been invested. After putting some money in a bank account with simple interest, I have the same incentive to keep it there after 1 year, or 5 years, or 10 years. I can withdraw the money, and reinvest it a year later, and lose nothing more than that single year's value in interest.
With compound interest, your interest payout goes up with each passing day/month/year, as your principal compounds and the value of the interest goes up. Because of this, my incentive to keep my money in the bank is constantly going up. I stand to earn more interest in year 2 than I did in year 1, so I'm effectively incentivized to keep my money in the bank for as long as possible, in a way that simple interest does not. If I withdraw money for a year, I'm missing out on that year's interest, plus all the future interest I would have earned on that year's interest.
Simple interest and compound interest rates could be set such that they have an equivalent payout, but only at a certain point in time. Before that break-even point, simple interest would pay more, and after that point, compound interest would pay more. A savvy investor could invest in a higher-yield simple interest account, and simply close it and reinvest or switch to a compound interest account that would have a higher long-term yield. Simple interest doesn't expressly prevent one from taking advantage of increasing principal, but it puts an onus on the consumer to constantly close/open accounts or expressly reinvest interest as principal.
Overall, compound interest is easier for the consumer since they don't have to muck around with their account to maximize interest, easier for the bank since the bookkeeping is simpler, provides a potentially larger long-term benefit to the consumer, and provides a means for the bank to incentivize long-term investments.