One thing a PC lacks, which is kind of critical for working with sensors and things, is easy access to IO.
A PC has a number of buses, but no GPIO pins. To get any form of GPIO you will have to add extra hardware in the form of PCI cards, etc. Those kind of things, since they are not widely used, are rare and hence expensive.
People have "hacked" their PC hardware before now to add I2C devices to the I2C bus that is present on all DDRx DIMM slots (used for module identification) and using that you could add I2C IO expanders to get some GPIO pins - however that is not easy to do, and then you have the problem of programming it on top of that.
The most flexible solution is to use USB. Using the PC as the "core" processor for heavy data processing, image capture, network communication, etc is simple enough and commonly done. Then using USB you interface to the devices you want to work with - cameras, etc. You can get USB-based IO boards which provide different forms of IO communication, such as TTL UART (FT232 boards, etc), parallel GPIO, I2C buses, SPI, etc. Of course, programming those things becomes somewhat tricky, and you may end up with a massive number of dongles on your computer to interface with the large number of things you want to connect to.
So a more flexible and sensible approach is to create your own USB interface to your sensors and other items. And one of the best and easiest systems to do that is, of course, the Arduino and Arduino-like boards.
An Arduino, or multiple Arduinos, become a sensor interconnect board which you program to communicate with whatever you need to communicate. That can then pass data back to the PC through USB which then performs the heavy number-crunching and what have you. Data can then be passed back through the USB to the Arduino for controlling other things (fans, lights, heaters, whatever).
So yes, you can use a PC as a powerful processor system in a larger plan, but the PC itself cannot replace an Arduino.
Of course, all this is assuming you have a PC to waste on the project, or you have the requirements of massive amounts of processing power that you can't get from any decent micro-controller or SoC.
One thing to remember: there are micro-controllers available cheaply today with considerably more power than the first pentium PCs - I regularly work with 200MHz MIPS based MCUs with embedded FPU - that's 3.33 times more powerful than the first pentiums (and without the floating point bug ;) )
The current Raspberry Pi embedded Linux computers provide all the GPIO and interfacing you should need at a tiny fraction of the price of a PC. They are (as of version 3) a quad-core 1.2GHz 64-bit SoC. The same quad-core 1.2GHz core that is used in many smart phones. That's more powerful than my laptop.