Wow, that is a long text, make it is a good topic for a dissertation
Good question, I have thought about the subject lately. It is somehow made of two parts.
1. Does the tds increase from fertilizers matter ? For most things no, it is too small a change to make a difference. It is likely a lot smaller TDS change than what most fish experience in their natural environment. Maybe fancy shrimps, but who knows ? that part of the hobby is even more filled with make-believe and hear-say than the planted aquariums. What increases the TDS is more important than the TDS increase alone... in this case, it should not cause problems
2.Is there any advantage to dosing daily vs one time per week ? I do not have any experimental data to prove this, from what I learned in the plant science uni lectures there are some educated guesses. They are however guesses... Plants adapt to certain (wide) concentrations of nutrients. They will produce extra transporters for scarce nutrients, extra storage organelles and chelators for abundant nutrients. Such adaptations take time from trigger to perfect adaptation to env. and require energy investment. This energy is somewhat wasted if you have overabundance at the start of the week and scarcity at the end. The timeframe for change is an important factor here as plants do not adapt from one second to the next to nutrient conc., or from one hour to the next. Is one week a short enough interval for plants to not adapt ? Under low light , low metabolism plants maybe. For high light, fast growing stem plants I thing the respond even from one day to the next.
What does this have to do with fertilizing once per week ? If you put in one day 30ppm NO3 and 3ppm PO4, your nutrient levels will go down to 0 towards the end of the week and then spike back up after the water change. Compare this to dosing daily where you might get some small amount of accumulation from one dose to the next, dropped down by the water change but quickly replenished by a nutrient dose. Or even better some heavy dosing immediately after the water change and smaller doses afterwards so as to try and keep some ~constant levels.
Next, as Zorfox stated precipitation of some element and/or bacterial uptake are things we have to deal with in the aquatic env. Most discussion is regarding iron and metal traces that depending on water hardness, PO4 levels, chelation type can be taken out from solution in hours or days or weeks. From the papers I have recently read, it seem iron precipitation is governed by PO4 levels ( more than the other way around). PO4 itself can also be uptaken and stored in unavailable (for plants) forms by bacteria ... maybe this explains why some people notice that even with 6ppm PO4 per week they seem to run out of it.
In short, regular dosing of iron and traces seems like a better idea. Macro nutrients are not likely to cause problems as long as they are available in abundant conc. throughout the week. Does the aquarium need to be dosed hourly ? No, but it makes sense to try and keep it constant (with some wide margins)