If you have a small business, the free tier doesn't add any value to your website. If everybody pays, the value proposition is very clear for everyone. Also, you need to consider that people, who use your service but don't think that the value of it can be expressed in terms of money, are not a good fit. They are a burden somehow. If they don't get enough value out of the service to pay a few euros a month, then you shouldn't do business with them. Of course, you've got a problem if nobody gets any value out of your service, but then you didn't have a good business idea in the first place.
However, I'd always add a trial period for new people.
I've heard things like Photoshop only having the amount of cachet it does in the professional world because of its ease of piracy for students. Sure the prosumers and teenagers who pirate are "not the customers you want" but it can be worthwhile long-term marketing. What's your thoughts on this?
Products like Photoshop are a relatively unique case in the sense that they are, in many ways, the only product. There are other other photo editing programs (gimp has actually gotten pretty good at this point), however there is a significant cost to re-learn how to use the new program. This cost to learn effectivly creates a lock-in effect, where the cost of Photoshop is cheaper than the cost of learning something different.
Additionally, Photoshop does not have ongoing costs with pirates. Whereas a web service needs to maintain the servers for the free users. And because Photoshop is pirated, the do not have an expectation of customer support.
However, I'd always add a trial period for new people.