In a perfect world the main sheet would only adjust the angle of attack of the boom, and never apply any downward force on the boom. All downward force on the boom would come from the vang, and in this perfect world the only purpose of the traveler would be to change where on the boat the force of the sail is applied to alter the force of lateral rotation (weather helm vs lee helm).
In reality no boat is perfect, and the main sheet applies mostly downward force on the boom when close hauled, and little lateral force as it should, So the traveler gets a 2nd job. That 2nd job is to adjust the angle the main sheet applies force to the boom, reducing the downward force, and increasing the lateral force. By moving the traveler to windward you are now pulling the boom from a flatter angle and just like anchor scope, the flatter the angle, the more power you get in that lateral direction, and the less you pull down (or up when thinking about the anchor).
Think of your anchor let out at 1:1 scope, you have almost no holding power at all, that's what your main sheet is like when it is straight under the boom. If you let out more scope on the anchor and you are now pulling sideways on the anchor, not vertical. Moving the traveler to windward is the same concept for the boom.
A common misconception is that the traveler is used to control twist, and not needed with a rigid vang, that is completely false. Travelers are ONLY for fine tuning the angle of attack, and adjusting the point of force against the hull (weather helm vs lee helm). Used properly a traveler will never adjust twist. You control twist (downward force on the boom) first and foremost with the vang, rigid or soft, doesn't matter (rigid does help to zero the weight of the boom in light air for a little better sail shape though, but they both address twist the same). You control the angle of attack with the main sheet, and you control the attachment point of the main sheet with the traveler. Any twist control from the main sheet is actually a by product of our imperfect rig designs (and I mean probably every boat ever made, they all compromise something for weight, ease of use, space, or cost).
Do you need a traveler? No, you can sail the boat without one, you just won't be able to control the main sheet as well as someone who has a traveler (and knows how to use it). The result will be over flattening the main when close hauled by applying too much downward force to the boom, resulting in slower speeds and/or your inability to sheet the boom in far enough reducing your inability to point as high as other boats with otherwise identical setups.