The reason they turned smite into a summoner spell was to prevent a lot of other classes from abusing smite items (Looking at you blue ezreal) which has been fairly successful outside of a few unexpected scenarios (Looking at you runeglaive Ezreal (also cinderhulk top meta))
Basically by making jungle items require the smite summoner to be bought it helps prevent other champions from dipping into the jungle line without making sacrifices.
If other champions could pick up said items without giving up summoner spells I expect that in high level play especially people would grab up smite items as laners to get teamwide objective control.
At that point you have to make smite items not worth it for other champions, either by hurting their stats (thereby hurting junglers) or by making them very expensive (thereby hurting junglers)
If smite became linked to the items that built into it I would expect to see a lot of laners building them. ADC's can very easily build the AS or AD items because they are highly efficient if you don't have to give up a summoner for them, and the challenging/chilling smite would provide a lot of tools for them.
Supports would stop building sightstone because they can just grab up trackers knife which also provides objective control.
etc. etc.
It would either completely tilt the meta on it's ear by making everyone get chilling/challenging smite, give teams up to 4k extra true damage on objectives, and throwing most other summoner spells out the window, or it wouldn't do that and instead just trash jungler's early games because the items would have to be trash for laners not to want them.
Even with the items being tied to smite many champions have already abused them. If laners were already willing to give up a summoner spell just to get at good jungle items then imagine how many would build it if instead of having to give up a summoner spell they got one instead.