First, I'll state the obvious: It's not an either-or.
Second, if you look at research on incentives, I think you'll find reducing everything to money tends to backfire, where people who used to go the extra mile in the past stopped doing so because they knew the amount of money they would get would be little.
Think of this scenario some of us have been in. A friend of mine who's big on cars insisted he change my oil for me. He insisted paying Jiffy Lube is a big ripoff. So he did the work, and then I tried giving him some money. He got very offended.
I needed to visit a city for some personal work for a few days, and stayed at a friend's place while there. I tried paying him a nominal amount for his hospitality. Result: He was offended.
However, in both cases, if I repay them by buying them coffee or a lunch, there would be no offense. From my perspective, the outcome is the same: I lose the same amount of money. But on their side, the response is drastically different.
I won't get into which approach is "correct" or "better". The reality is that, in most societies, including the US, the majority behaves this way.
Dan Ariely in one of his books talks about the research involving what he calls "social" vs "market" contracts. The former is usually non-financial, and often involves favors we do for friends. The latter is usually precise and monetary.
Now of course, it depends on the type of work you do, but for most salaried positions, it is a mistake to assume that only market contracts apply ("I do work, and I get paid for it"). What Dan Ariely's chapter shows, is that when companies do lean towards mostly market contracts, bad things happen: Poorer productivity, fractious work environments, etc.
Even if you're getting paid, there is a place for both types of contracts. If you're one of those who care only for the amount you get paid, you're definitely not someone our team wants to hire. I've seen this even within my company - one org takes care of both contracts, and another doesn't. I used to be in the latter and I'm glad I left for the former.
In my company, we have a tool where any employee can thank any other employee with a greeting card. The recipient's manager is notified. The "thanker" can attach company money to it (almost always do) - a nominal amount. Anything over about $30 needs to be approved, but anything under is provided without managerial approval - the company just provides a fund for this.
I think it works well, and in my department, we are frequently encouraged to thank others using the tool for both big and small things.
It doesn't impact your annual review at all. You still have the usual process to get a raise, promotion, etc.