It's actually the right approach, if you're A.) looking for the best bang for your buck and B.) capable of buying all of those parts and assembling them yourself. But most of the time, people who ask for recommendations are neither of those two things; people who are skilled enough to assemble an entire desktop PC from individual components are already knowledgeable enough about these things that they no longer need any help nor recommendations.
The Best Bang for Your Buck isn't Always the Best Choice
You tend to hear this phrase a lot if you ask for recommendations online: "if you just spend a little more, you can get this [model], which is going to be 10 times faster and sturdier than what you're looking at."
Many businessmen/entrepreneurs already know this part by heart - there are a lot of times when people aren't interested in products that are inexpensive when compared to what you are getting for the price. In fact, a lot of times people are only interested in the price. Partly because people have a slightly skewed sense of value, and partly because there are people who simply don't have the money: if a person only has $50, it doesn't matter if the $60 product is one hundred times better. He's only going to buy the product that he can afford, the $50 one.
Prebuilt PCs will not give you the same "quality relative to price" ratio as assembling your own PC does, but it usually ends up being significantly cheaper mainly because it's purpose is not to give the best bang for your buck. It sometimes includes parts that are not as good or even gimped. But normal users can get by on these parts.
For example, an enthusiast may pass on a cheap motherboard because it doesn't allow them to set the clocks higher than the manufacturer intended, or because it can only accept one videocard. Normal users don't overclock, and don't really need dual videocard setups. The cheap motherboard on the prebuilt will be fine for them.
Installing Components On Your Own is Not Always a Good Thing
Granted, if you were able to cherry pick the components that will go into your PC and install them yourself, you'll have more control over the final results and can literally get the best sum of all parts. However, it hinges on the fact that you know how to install the parts, and that you have enough manual dexterity to avoid ruining stuff on your own.
This is where prebuilt desktops have a true advantage. The person who's going to put the parts together for you is going to be an employee from the place you bought it from. The benefit is more than just convenience. If you're installing parts on your own and you accidentally snapped the small tab that holds the CPU in its socket, you're pretty much SOL. The tab is too small to fix with superglue (and superglue isn't strong enough to hold it in place anyway). On the other hand, if the person who's assembling your pre-built PC messes up and breaks something, you don't have a problem. The store's going to replace it and you'll be none the wiser.
Things You Need to Do When Getting Your PC Built
Of course, there's a tradeoff and you're not going to get everything on a silver platter just by lowering your expectations. There are a few things you need to do in order to avoid getting a pre-built lemon, such as:
1. Don't Leave the Store - you don't really need to constantly look over the technician's shoulder, as that would be plain rude. But never EVER leave the store while your PC is getting assembled. For one thing, leaving will encourage the technician to slack off. Building one from scratch (trust me, I worked as a technician for 4 years as my first job) doesn't take longer than an hour and a half so it's not going to be much of a wait. Next, it deters any malicious attempts (like, you know, replacing the parts with even cheaper ones or pocketing them entirely. It happens.) and more importantly, you need to be around to do some of the stuff in this list later on.
2. Ask for a True Rated Power Supply - this will cost a little bit more money, but it's very important. Prebuilts usually rely on the cheap power supply that comes with the case. Said power supplies are very unreliable, and if you're going to splurge on a part, the power supply has to be it. An underperforming power supply will (not can) eventually resort in random restarts, erratic performance (some random hangs and freezes that people blame on virus or slow cpus are actually the result of a power supply not being able to supply enough juice). What's even worse is that if you install a new component, or even if you just plugged a power hungry device on the USB when the power supply is already straining, you'll hear a hiss and a pop (the sound of a mosfet exploding), which means the motherboard is now dead. And that is if you're lucky. It could take your hard disk, videocard, and CPU with it.
3. Try to See If They Left the Foam Padding Under the Motherboard Behind - this is too specific that it seems out of place, but it's sadly a common occurrence. A lot of technicians tend to install the motherboard with the foam padding underneath still intact, under the mistaken idea that it will help prevent the motherboard from touching the metal plate (and shorting out). First, if you install a motherboard correctly, there are metal pegs that will prevent it from ever touching the backplate. Next, the foam padding absorbs heat extremely well. Couple that with being placed underneath several heat-producing components such as the processor and the Northbridge chip, and you'll have a PC that's prone to overheating during extended usage (the heat absorbed by the foam can't be dispelled by any of the heatsinks or fans inside the case).
4. Ask if You Can Test It Before They Put It In the Box - Even if you're not tech savvy enough to know which one to test, do it anyway. First is that it keeps the technician on his toes knowing that you're going to check if he did a good job, next is that simply trying to use it for a while, even if it's just to type DIR on a dos prompt or move the mouse around will let you rule out a lot of destructive mistakes, like that one time when a coworker was too lazy (or absentminded) to organize the wires inside so when the PC was booted up, one of the wires was touching the case fan and got cut up pretty bad, resulting in a little bit of smoke coming out of the PC.
5. Last But Not the Least, Check if the Driver CDs Were Included in the Box - these past few years, it has become more and more common for people to leave out the discs containing the hardware drivers. Part of it is because some people are too absentminded, and part of it is because they thought, Hey, she can just download it off the Internet. Unfortunately, in some cases you can't download stuff from the Internet because the things you need to access it - the LAN card or the WiFi modem - doesn't have a driver yet. You can get it from another PC, but usually it is less of a hassle to just remember to check if the driver disc was included.
...and there you go. Hopefully, if you keep the above things in mind, you don't have to worry about buying prebuilt PCs in the future. Sure, it won't run Crysis nor will it manage a 4.5 Ghz overclock, but it can let you do your work and browse the net, and it won't cost as much as a second mortgage.