I think Erin has done an excellent job with his latest video about building a budget system:
He hasn't shown any such "building." He is throwing a paper design at people. No way you can throw a sub in the room and expect it to blend properly with another random speaker. Have him show the combined measurements of such a system in a room and then we can talk.
He is using most if not all of them for the speaker correction. That is just wrong. Room modes needs to be taken care of and they would easily cost you a pair of filters.
If you want such a budget system, forget about the sub. Get a speaker with smooth response that maybe needs a single PEQ filter. Then measure your room and optimize the bass using filters in WiiM Amp.
And no, I don't remotely buy that 1/3 octave smoothing in that phone app is going to give you any kind of useful data to fix room modes. It simply is not the proper tool for the job (room modes can be as narrow as 1/12 octave). People should spend the $100 on microphone and use REW to measure and optimize the room properly. That will make a huge difference in how clean and open the system will be (fixing room modes).
BTW, instead of bookshelf, I would get a low cost Tower speaker. They would be more sensitive, extracting more use out of the limited power of WiiM Amp. And you might get a bit deeper bass which would be another reason to not bother with a sub.
Really, this notion that you just "add a sub" needs to stop. It complicates system design tremendously and forces a novice user in this case to become a speaker designer. For a theater, sure, you need one anyway. But for 2-channel listening, it is not a good idea.