What is it about certain business types that seem to restrict how much large they can grow? For example, I've never heard of a large lawn-mowing corporation. Phone and computer repairers seem to consist mostly of 1 or two man operations. Wedding planners and photographers seem exclusively to be home businesses. 

Why is it that certain types of businesses seem never able to grow into a large company? I'm assuming if it were possible, at least some percentage of lucky or savvy businessmen or women would have found great success.
That's a very interesting question and there are multiple potential reasons for this.

One reason is that production is simply not efficient at a larger scale. There are diminishing returns to scale: i.e. doubling inputs will result in less than twice the output. This means that two smaller production facilities can be more efficient than one large one.

One way to think about this are kids shoveling snow in winter. Beyond a certain number of kids with shovels they're just going to get in each other's way shoveling the same driveway. Now they could of course split up into two or more groups, these two groups could be one firm or these could be two firms. But what's the rationale for combining these two firms into one? They probably will not economize on any fixed expenses. They need to ring the doorbell, bring their shovels, and ask people whether they wish their driveway to be shoveled. Sure one kid could specialize in negotiating a price and ringing many doorbells and scheduling appointments, but 
the gains from specialization are probably not such that it's worthwhile. It's not how that "industry" works. You ring, you shovel, and you move on. So there is no good reason for combining. The kid ringing and making appointments is an unnecessary overhead. It's better that he shovels too.

Another reason are the fixed costs of certain regulations. You're probably familiar with the fact that in some jurisdictions firms above a certain size need to provide certain services to their employees. If you're a small firm, then you will incur that fixed costs all at once if you expand over that threshold. You'll have to get your existing employees those services and the new people. These additional fixed costs might not make it worthwhile to hire extra people unless you can be certain that you can expand your business well beyond that. 

A third reason is that many people do not want to expand their businesses. They enjoy the work that they do and the extra income is not worth it. They'd have to spend less time doing the work that they enjoy and more time on administrating the work done by others. Effectively this is a change of employment. So you might as well ask why do some people do work A and not work B?

These are three reasons. The reasoning is the same each time though. The benefits of expanding do not justify the costs of expanding in that particular situation. Given that there are many different situations there will be many different reasons why people choose not to expand their business. 

Does this answer your question?