Relevance of memory reads while calculating the time complexity of an algorithm
For a memory read to be relevant to the algorithm, the information read in must be processed in some way.
If the information is never compared or used as input to any operator, it will not affect the algorithm and thus was unnecessary to read in the first place.
If there were an operator that could accept a variable number of inputs, a number that could grow without bounds, then and only then could you have the number of memory reads far outnumber the number of operations in the way you describe.  For instance, if &quot;sum&quot; were a single atomic operation accepting any number of inputs, then you could have such an algorithm.
However, a model of computation where a single operation could utilize an unlimited number of inputs is not very interesting nor very useful for algorithmic analysis.  It would essentially just push all the hard work to a lower level of abstraction.  So you won't find such a model in any CS literature.

A paragraph from an MIT Open CourseWare PDF about communication networks as in Graph Theory makes a related point (related to what I said about just pushing the hard/interesting work to a different level of abstraction) in discussion of switch sizes:

One way to reduce the diameter of a network (and hence the latency needed to route packets) is to use larger switches. For example, in the complete binary tree, most of the switches have three incoming edges and three outgoing edges, which makes them $3 \times 3$ switches. If we had $4 \times 4$ switches, then we could construct a complete ternary tree with an even smaller diameter. In principle, we could even connect up all the inputs and outputs via a single monster $N \times N$ switch, as shown in Figure 6.9. In this case, the “network” would consist of a single switch and the latency would be $2$.
This isn’t very productive, however, since we’ve just concealed the original network design problem inside this abstract monster switch. Eventually, we’ll have to design the internals of the monster switch using simpler components, and then we’re right back where we started. So the challenge in designing a communication network is figuring out how to get the functionality of an $N \times N$ switch using fixed size, elementary devices, like $3 \times 3$ switches.