Problem #1: virtually no freelance/independent contractors psychologically value the equity as equal to (let alone greater than) cash. To most people, 5% equity in a startup sounds like a very small amount, so they may demand 10% or accept 5%, but view it as a token amount. That leads to not prioritizing your business/project over cash-in-hand opportunities.

This means you could give 5% to a web developer, who you have to harass endlessly to prioritize your work, resulting in your being 3 months later to market. Eventually, if you succeed via your hard work, the company is worth $1M, so you ultimately paid $50k for a website and the developer never valued the equity anywhere close to what it's worth.

Note: it's not just undervaluing equity that leads to a lack of priority, many freelancers live on a short financial leash. The ones who are rolling in cash and charging top rates often don't have much incentive to take equity in a startup or they'll take equity alongside a reduced cash rate.

Problem #2: very few specialists are good long-term business partners. Do you want them seeing your financial statements? Do you want to explain financial projections and business decisions to your web developer? Want your accountant involved in management, marketing or hiring decisions? Would you put them in front of an investor or let them review a term sheet? Would you want them voting on your board of directors?

As the majority owner, you can't simply ignore minority owners: http://venturebeat.com/2011/07/18/what-are-the-rights-of-minority-stockholders/

Problem #3: most people (founding entrepreneurs included) are impatient. Everyone thinks their equity is going to be measurably more valuable in 6-12 months and the reality is it usually takes 3 years or longer to build a company that anyone would acquire. Is that service provider with equity going to be frustrated by the actual timeframe and constantly pester you to buy him/her out?

Problem #4: if you complicate your cap table with a few people who were short-term assets, that sends potential investors a message: you didn't value your equity, so they are going to grind you in valuation negotiations. They will also include term sheet clauses that are lopsided (including stronger than usual board representation) because they figure you're not savvy enough to negotiate them out. Also, if the cap table is perceived as too complicated, some angel / VC investors simply will pass because they don't want the hassle.

Conclusion: I've seen these situations pretty often and most go badly, so if you think I'm generally down on the concept, you'd be right. I would be remiss if I didn't say it can work well, but only if you are gaining a true long-term partner who wants to be involved in ownership of the business long-term. If the person simply has some non-billable capacity and is viewing your equity as a lottery ticket, definitely pass.