tl;dr:
Do I need a merged patch?
Yes!

But I already have a Bashed Patch
You still need a TesEdit merged patch. Bashed patches only contain leveled lists. Merged patches contain lots of other stuff too,

How do I make one?
Load all your mods (minus things like skyproc mods that have dynamic patches) in tesedit and wait for the finished loading message. Then right click on a blank space in the left panel and choose create merged patch. It will say its not supported but click ok, then give it a name. It will work for a while and eventually make a new esp with the conflicting records merged together. Make sure you save it when you exit. Then activate it in your load order and make any dynamic patches like automatic variants or DSR or reproccer. You might have to add a BOSS user rule to make sure the merged patch loads before those.

But I've heard merging mods is bad. What gives?
That kind of merged patch involves renumbering formids, like the script does, and just mashes the contents of separate mods together. Its only useful if you have more than 255 mods since that's the limit of the number of esm/esp files skyrim will allow. It only works on simple mods since if they involve scripts or complex references between entries they will almost certainly get messed up.

So give me the long version.
I'll break down what a bashed/merged patch does since its kinda complicated. Skyrim (and other beth games) stores all the information about game objects in the data files where each object has its own record. So in Skyrim.esm there is an Ulfric NPC record with everything about Ulfric. Other plugins can modify existing records to change what shows up in game. So for example Dawnguard.esm could give a new perk to Ulfric. The trouble comes when you have multiple files that change the same record. Skyrim only sees the data in the last loading file, all previous conflicting entries are discarded.

So if you have a mod that changes Ulfric's skin color to be black and a different mod that gives Ulfric a fancy hat normally you would only be able to see one in game. The merged patch bypasses this and lets you have a black Ulfric with a fancy hat. It does this by reading every file in your load order and comparing the records. It will see that Ulfric from Skyrim.esm is in your two mods so one is being overwritten. But it can also see the overwritten changes don't actually conflict so it makes a new mod (the merged patch) that contains Ulfric from Skyrim.esm and adds the black skin from the first mod and the fancy hat from the second mod. Then when you start the game you see a dapper black Ulfric.

If you added a third mod that made Ulfric albino that would be an actual conflict between mods. Obviously Ulfric can't have both black skin and white skin. This is where the difference between TesEdit and Wrye Bash comes in. TesEdit resolves those conflicts based on load order. If albino Ulfric was after black Ulfric tesedit assumes you want to see albino Ulfric in game. Wrye Bash allows specific instructions not based on load order in the form of bashed tags. So you could add the tag for skin tone to the black Ulfric mod and when the bashed patch was made it would make Ulfric black even though albino is after it in the load order.

But Wrye Bash is gimped for Skyrim. It only works on leveled lists* so your bashed patch wouldn't contain anything about Ulfric at all. Tesedit works on leveled lists as well as many other record types like weapons, armor, and npcs. So if you make a bashed patch and then load a merged patch after it the merged patch will overwrite the leveled lists just like any other mod. If you want to use bash's lists the correct way is when you make the merged patch find the leveled lists section in tesedit and delete it. Then it won't conflict with the bashed patch.

*Wrye bash can do a few other things with a bashed patch like combine minor mods into it. This lets you disable the combined mods which is useful since skyrim can only load 255 esm/esp at once. I think it might also allow minor tweaks to settings too.

Why does tesedit say merged patches are unsupported?
If your merged patch contains changes from an incorrectly made mod skyrim will crash. That's not the merged patch's fault its skyrim/the mod's. The tesedit team was tired of complaints about it so they put the warning in.