Do you want the completed quilts? If not, why not donate the blocks to a group who will turn the blocks into quilts and get them to a needy recipient?
My thought is if you store the blocks and set them aside so you can make more blocks (the process you like doing) you will end up with boxes upon boxes of completed blocks that will never become tops, let alone quilts. If you honestly feel you will assemble the blocks into a top and complete it into a quilt, there is absolutely no reason you can't store them as blocks with the fabric you will use for sashing, border and binding and the backing if you are particular about that.
We all have favorite parts of quiltmaking and parts we don't like at all. Some of us persevere through to get the completed end product, a usable quilt or wall hanging. Others are perfectly content to have unfinished tops that may or may not get around to being quilted. Loads of us work on several projects at once. I have WIPS and UFOS in all phases of construction from completed top waiting to be quilted to just the fabric and pattern set aside and everything in between. Once a quilt is quilted I do continue to work on only that quilt until it is completed by putting the binding on and a label and a hanging sleeve. I suspect there may be quite a few out there like you, who only like making the smaller units, the blocks or maybe even parts of blocks. That is pretty obvious from the numerous postings on the QB of thrift store finds of blocks and partially assembled blocks. If you have no desire to have the completed quilt, I say donate them to a guild who will complete them and get them to a worthy cause. If you do want the completed quilt store them as blocks. If you don't ever pull them out after five or more years, donate.