The tiller rubbing against the lazarette hatch is an annoying problem not addressed by the current design. I have not seen a significant issue with wear on the tiller or the hatch on my boat. It also strikes the coamings on either side. Just an "S" thing.
As purchased (used) with my tiller, there is the tiller post, a sleeve that rests within the post to prevent distortion of the post (AKA the Rudder Post Crush Bushing, missing in your photo but available from Blue Water Yachts -
https://shop.bwyachts.com/product-p/5210-1c3.htm),the two plates that connect the tiller to the post, the bolt that passes through the connector plates and the tiller post, and the nut (ideally self-locking, which yours appears to be) that holds the bolt in place.
The holes in the post get worn over time, causing a significant amount of slop between the tiller and the post which is
very annoying. One remedy is to tighten the nut on the bolt that connects the tiller and post, but that is a poor and very temporary fix and could distort the post. I made some shoulder washers from bushing material purchased at my local big box that help snug things up, requiring occasional tightening of the nut (see attached photo).

I made the bushing by taking a bronze sleeve that fits as closely as possible over the connector bolt, chucking it up in my drill, and grinding a chamfer in it by pressing the tip against the a grinding wheel while slowly spinning the bushing with the drill. I cut the chamfered portion off with a hacksaw and cut a split in it that would allow it to conform to the diameter of the bolt as it is being forced into the holes in the post, making one for each side of the post. They go between the side plates and the holes in the post, which is a pretty fiddly operation helped by holding them in place with masking tape while re-installing the tiller and plates. Even with a self-locking bolt, it needs re-tightening from time to time and the bushings can wear out as well.
Once you get that crush bushing from BWY (or make your own if you are so inclined), I recommend taking a stout twist tie (like one you can save off a coffee bag) and using it to keep the bushing from falling down into the tiller post. I leave this in place to facilitate repairs and maintenance.
I am stumped on a fix for the tiller/lazarette cover rubbing thing unless something comes to me in a dream. Any fix at the post would be subject to a lot of lever-arm-distance force, so would have to be very stout. I'll have to put on my thinking cap on that one.
The key to inner peace is to admit you have a problem and leave it at that.