For me it is clear that warscrolls have nothing to do with the units on the board but telling you what you can do with them. Otherwise one would have to say I'm taking like 5 warscrolls of saurus warriors to play 5 units of them. The point would be that if you agreed to limit the number of warscrolls (and so the number of Different(!) units you use in the game) and you have for example decided not to take razordons you should not be able to summon razordons. But as I see it that would be more like a house rule, due to the fact that there is no point system or something like that in AoS.
I would agree in theory with what your saying, however the Laws of War (which you can see in another thread) specifically state taking
duplicate Warscrolls is a source of power (meaning that it counts towards your overall power, which dictates how strong your army is compared to your opponent). Now I don't know if these have been officially published, and thus might hold no authority, but this clearly indicates that each unit is intended to have its own Warscroll, and that Warscrolls are intended to be a restricting factor (GW stated that these rules were best suited for games using 3-10 Warscrolls) in the types and quantity of units you can field. So yes, to use 5 units of Saurus you would need 5 Warscrolls.
So really your entire collection of minis are in reserve the entire time.
Whilst the various summon spells do not state that they are summoning units from reserve, this is effectively what they are doing.
Fate is lending a hand as it were.
I had considered that position as well, but I still found it to be worded too incorrectly for me to agree to it. There are other methods in which these reserves can come into play through non-traditional summoning (Chaos Lord ability special ruleset for summoning daemons, and scenario specific rules). And this could still apply if you needed a unit on the table, as several more units might be "in reserve".
It just seems to me that this system is too vague to have been intended that you could summon any unit from your theoretical army. Especially since bringing your whole army is intended for deployment purposes (you are are suppose to react to what your opponent brings, one unit at a time, instead of making a predetermined list). This also protects from sudden death abuse (1 Slann start, summon whole army later).
If they wanted you to summon whatever you wanted there were much simpler and clearer ways of doing so (such as the keyword system I mentioned in an early post in this thread)
However I fully admit that I could be completely wrong. This is GW after all, and their official response will likely be like "use whatever interpretation you and your opponent can agree upon, and roll if you cannot".