Now, speaking of applications...
I've just been doing exactly what I described above as a typical application: building a subcircuit on a solderless breadboard to verify a concept that I had previously designed and verified in simulation. Simulation worked fine, but I needed to make sure that the power-on transition worked as I needed and just to test that it all generally worked in hardware.
The circuit involves debouncing two push buttons, which is implemented with some RC delays and 74LVC schmitt trigger input inverters (a hex inverter 74LVC14), and producing a single ~10 μs pulse per one button press. These pulses are fed into the inputs of an RS latch built of discrete 74LVC1G00 NAND gates, which do not have schmitt trigger inputs.
The part where the buttons and the outputs and inputs of the hex inverter IC were wired with short jumpers and resistors (even with uncut leads) worked just fine. But the RS latch part was built on a second breadboard (imagine the potential ground loops!) and while the Reset signal wire was short, the Set one was about 15 cm long in total and in addition made of two joined in series (connected on the breadboard).
Guess what, it failed: when the Set button (long wire) was pressed, the RS latch gates went into a state where apparently the CMOS output transistors were cross-conducting (the PSU went to CC mode at ~20 mA, so no ICs were harmed). Curiously, though, it went out of that state on the second press of that button. The Reset button, whose signal was sent over a short wire, worked fine.
What caused it? Well, if you send a pulse with a sub-nanosecond rising or falling edge over a crappy 15 cm-long wire that's terminated with whatever the solderless breadboard has to offer (not to mention the return path), you can guess what beauty the receiving end will see :).
Solution? Easy: add a series resistor right after the output pin to make the edge slower and thus reduce the reflections to more or less return the pulse to a good shape. Even as small as 47 Ohms one solved the problem (even though the signal seen by the scope at the target input pin was still ugly, but apparently good enough).
Conclusion? Know what you're doing and what can be causing the issues you're seeing and how to solve them to mitigate the limitations of your tools. And if you don't know what you're doing, still do it! Encounter problems, troubleshoot, search, read, learn, run simulations, and you'll know what you're doing the next time.
And of course it took much less time than it would have with soldering. Zero mess, zero fumes. Easy to fix mistakes, easy to hand pick and try various values of passive components. Solderless breadboards are cool*!
*but you'd better have an assortment of ZIF socket to DIP adapters for SMD stuff.