Yes you need a splitter. The headset jack combines the mic, left/right, and ground into a single plug. If you plug it into a left/right headphone jack it'll work since those parts of the plug line up with a regular stereo plug. But the mic will not work in the mic jack since the part of the headset plug for the mic gets mapped to ground on a mono microphone plug. The splitter will map the mic signal to the correct part of the plug (the tip).
Edit: Be aware that the headphone/mic splitters and the 2-to-1 splitters can look identical. To be sure you're getting the right ones, try to find a model which has a picture of headphones and microphone on the two plugs. Different colors is also usually a good indication you've got the right cable, but not always.
https://www.amazon.com/dp/B071NDLCGC/
And the reason combo jacks aren't the norm on PCs is because putting the wires so close together can cause crosstalk (some of the audio being transmitted over the headphone wires gets picked up by the mic wires, and becomes audible on the mic channel). So you always want the two separated whenever possible. The devices which use combo jacks do so because they don't have the space for separate jacks.