Guys, we're talking about a service tech here, not a homeowner. A once a week visit is a completely different situation than being able to add chlorine to the pool every day or two or even twice a week if a mostly opaque pool cover is used.
If you don't want to have a high CYA and do significant FC swings using chlorinating liquid, say from 14 ppm down to 4 ppm using 100 ppm CYA (which companies such as
Pool Chlor do), then some form of algaecide or phosphate remover is going to be needed if you don't have any chlorine dosing during the week. You can view a phosphate remover in the same vein as an algaecide. They both prevent algae growth, but in different ways. A phosphate remover is generally expensive, but if the pool water doesn't get additional phosphates added to it then it may be mostly a one-time expense to remove phosphates. Check the phosphate level in the tap water looking at the municipal water quality report since phosphates are often added as a corrosion inhibitor. Note that HEDP metal sequestrants add a lot of phosphates to the water so you don't want to use this approach if you've got metal in the water and need to sequester it.
Another approach to keeping algae at bay is to use Polyquat 60 algaecide and that is something that should last through the week, but it must be added every week.
Even with the above techniques to prevent algae growth, an outdoor pool with chlorine is unlikely to have the chlorine last through the week unless you start with a fairly high level. Note that though 14 ppm FC sounds high, with 100 ppm CYA it actually isn't that high and is roughly equivalent to around 0.15 ppm FC with no CYA in terms of the active chlorine level.
This is why many service techs use Trichlor pucks in a floating feeder or inline chlorinator. It provides continuous chlorine, but with the downside of increasing the CYA level over time. If you don't raise your FC level as the CYA level climbs and don't use an algaecide or phosphate remover (or are lucky with water very low in phosphates), then the pool can get algae. The pool store I go to in my area services over 2000 pools out of two store locations and they use the Trichlor approach with a 4.5 ppm FC target and they do a partial drain/refill when the CYA gets to 100 ppm. Some of the pools get algae as the CYA gets high (no surprise here) and they use a phosphate remover when that happens. So everyone has a somewhat different way of handling this, but the basic principles of why some methods work and others don't are the same.
If the pool has a saltwater chlorine generator, then there is no need for any algaecide or phosphate remover, but you do need to follow the FC and CYA recommendations on this forum since the manufacturer recommendations of 1-3 ppm FC with 60-80 ppm CYA is not sufficient to prevent algae (it should be 4 ppm FC minimum with 80 ppm CYA). See
Water Balance for SWGs for more details.
As for colloidal silver, I don't get the point of using that. I could understand using copper to prevent algae growth or a combination of copper and silver to prevent both algae and bacteria, but such products can result in metal staining of pool plaster unless you are very careful with the level of metals and keep the pH from rising too much.
As for the shelf life, it's essentially forever for the lanthanum chloride in phosphate removers, but those that also have built-in clarifiers (such as those from Natural Chemistry), the life may be shorter, but I'm not sure. For colloidal silver, the silver will last a very long time, but I don't know how long the colloid will remain in that state.
On this forum, the approach for residential homeowners is one of only adding what you need to the pool and doing minimal maintenance that is reliable, but this is more frequent when adding chlorinating liquid or bleach. By not using stabilized chlorine as a regular source of chlorine, the CYA level is stable and one can then just keep a proper FC/CYA ratio to prevent algae growth. No algaecides, no phosphate removers, no clarifiers, no flocculants, no enzymes.