ICs and external resistors

Many integrated circuits require fixed value external resistors and capacitors on some of the pins to work properly.

Why don’t they integrate those as well into the IC?

Capacitors are hard to make small, their size being constrained by simple physical properties. So they are quite difficult to put on a chip. The processes to make a capacitor on chip are not always compatible with the rest of the chip manufacture, and may add cost and complexity. Capacitors of any useful capacitance may be much larger than the entire chip they connect to. On chip capacitors are usually only a single layer of dielectric, so only very low values are possible anyway. Electrolytic capacitors are impossible.

The common capacitors are power supply bypassing, and the physical layout of these capacitors can be important. In addition to the simple size of the capacitor, it my not be a simple matter to connect it correctly on the wafer. You may need the properties of a multi-plane PCB to make them work properly.

Resistors may be used to program the functionality of the chip, and thus putting them on the chip means it can only do one thing. Whilst you may see a fixed value, this may turn out to be only in one application note, and across more chip uses, you may see different values. On chip resistors are not actually all that wonderful quality wise anyway. If the resistor needs to dissipate anything more than trivial power you don’t want it on the chip, and if you want precision, or very high linearity you want it off chip. (Some chips do have laser trimmed resistors, but this adds to the cost.)

Small resistors have a problem with high power levels. You can make a small 100 ohm resistor, but it will burn up if you jack lots of juice into it really fast. A large 100 ohm resistor that has plenty of surface area and air around it to dissipate heat will do better.

Oh, and resistance is futile anyway.

And, often the value of the external resistors and capacitors change the function of the device.
Either timing, or filtering or voltage / current reference.

I could imagine in some cases that the resistor/cap value may be determined after the chip has been made. By having it external, you don’t have to spin new ICs to tweak it.
-D/a

The 555 timing IC has three 5K resistors integrated. I guess there are just tiny currents passing though them.

If you look at this schematic, the 555 has a lot more than five internal resistors.
The 5k’s I assume you are talking about are in series with the supply voltage, so the current through each one is Vcc/15,000 or .3mA for a 5v supply. Note that these resistors are used to set voltage reference points, at 1/3 and 2/3 Vcc.