The only issues running most newer computers is potentially stability issues from the operating system, but newer operating systems tend to be good in the regard. The other power be power consumption, but the newest hardware typically also has very advanced power save features that make it not really a big deal.
There is no real longevity issue on keeping it running 24/7 unless it is overheating or something. If anything, I believe it is better for it to be constantly running than turning on and off very often, something about draining the power out of components completely then loading them again on startup putting slightly more wear on the electrical components. But I'm no electrical engineer. I ran a 2008 machine 24/7 for 4 years before replacing it, and I ran that thing hard, 8+ work hours a day, minimal restarts, never sat offline for more than a few minutes. And it still runs fine except the case wore out, the power button failed, so I stick my finger on the power pins on the mobo to turn it on now. Also a ball bearing is failing on the cpu fan...lol. But run it for 20 minutes and the ball bearing stops making noise.