I've been tested for Vitamin D deficiency. Because I had symptoms of osteomalacia. I needed high dose supplementation - which wouldn't have been prescribed to me without the test to confirm the deficiency. Most people in the UK (as a result of epidemiological research) have been found to have a milder deficiency/suboptimal levels and therefore the recommendation is to proactively supplement at a much lower level and therefore stop the deficiencies before they cause clinical symptoms. It's also being looked into as a potential cause of MS, as research has found a higher incidence in people who have low levels/live in places where the weather is worse/have lifestyle factors that make the sun an unlikely source.
Iron supplementation is only prescribed when a FBC has established that somebody has anaemia. Most people (as found through collating results of all the blood tests performed) do not, but some groups have been found to have a higher incidence (pregnant women, those with heavy periods, those with eating disorders, for example), so they are recommended to try to improve their diet, but will be prescribed supplements if necessary. Previously, the role iron played in anaemia, the fact that pregnant women tend towards anaemia and that it's associated with post partum haemorrhage incidence was found through research.
All women (thanks to that epidemiological research) who are thinking of becoming pregnant or are pregnant are recommended to supplement with 400mcg folic acid to reduce the incidence of neural tube defects - a cause and dosage established through the use of large scale epidemiological research. They don't test first because the data suggests that most women need to do it and it doesn't cause harm to have more (unlike vitamin A).
Epidemiological research has established that it is good practice when treating somebody admitted to hospital but suspected of abusing alcohol long term with a drip containing Pabrinex, a combination of vitamins (C and B1,2,3 & 6) that have been established (through research) to be almost universally deficient in people who abuse alcohol and are associated with various diseases. It's therefore not essential to test first, as the alcoholism is evidence enough to make it sensible to supplement in any case (and again, if they aren't deficient, all they'll do is excrete the excess with no harm done).
Research has also established that serum retinol levels do not correlate with symptoms of vitamin A deficiency unless they are extremely high or low here. The guidance is to look at exacerbating factors and seek advice from specialist teams, rather than supplement more than the level provided in Healthy Start Vitamins - and formula is supplemented in the UK exactly because it's been found to reduce the incidence in bottle fed babies.
We don't insist that babies are tested for Vitamin A deficiency before being given formula rather than a bottle of semi skimmed. We expect to give them formula if breast milk isn't an option. We don't supplement everybody because too high an intake is equally risky (more so in terms of teratogenicity).
I think you're reading too much into it/not taking into consideration that not having personally experienced having tests prior to supplementation doesn't mean it doesn't happen (or it does), so it doesn't really help support anything but that public medicine works.