If you follow standard laboratory practices, you would never re-use a disposable syringe either. So, by that argument we should be discarding the still partially full syringe, and using a clean, new syringe for each test! Taken a step further, we should also be "conditioning" each new syringe by initially filling it with the reagent, discarding that reagent, and then filling it a second time to do the titration.
Sure, absolute best practice would be to discard the reagent. But, as a practical matter, I must wonder aloud where this mysterious magical "contamination" is going to come from when using the same syringe for the same reagent for the same test each time? If someone is able to get, say, 70 tests out of a kit designed to give 50, then where's the harm?
With regards to a clean syringe every time you run a test: YES. You are absolutely correct.
As far as “conditioning” the syringe, that depends on the size of the variability introduced by not doing it and whether the reagent actually affects the surface. A glass surface with all its hydroxyl groups might need “conditioning”. Plastic has a rather inert hydrocarbon surface and unlikely to require conditioning, but good to check on the compatibility of the material of construction.
Disposable equipment is disposable because it is cheaper than non-disposable equipment that requires manual labor to clean. Disposable equipment does not necessarily get used up or degrade with use, unless it is the markings on a syringe or flask, the stiffness of the rubber tip on the syringe plunger, or the sterility of plastic equipment.
So, a clean, re-used one-use syringe can be OK for the frugal analytical chemist.
Not cleaning the syringe introduces the possibility of reagent decomposition, for example, air oxidation, CO2 absorption, and bits of concentrated reagent on the surfaces. It does not guarantee a disaster, just increases risk of variability. Not cleaning the outside of the syringe pretty much guarantees contaminating the reagent with the test solution. Not a guaranteed disaster though, more like Russian roulette with a BB gun
Getting seventy tests instead of fifty tests? We’ll need some real numbers before we kick this idea around.
By the way, is the cost of test kits really that big a percent of the annual cost of owning a reef tank? What about electricity? Salt? Food? Additives?
If you are really, really, really interested in lowering the cost of testing, reduce the size of the test sample by half or one third where possible.