Pairwise t-tests may lead to accumulation of type 1 errors.

an anova is preferable

e.g. see this explanation

https://statistics.laerd.com/statistical-guides/one-way-anova-statistical-guide-2.php

Comparing multiple means to a control is often accomplished with Dunnett's test.  An adjustment is often made to p-values (or alpha values) from this test to account for the fact that multiple tests have been performed.

Dunnett's test is usually performed after a significant anova result, and is therefore considered a post-hoc test.  I don't know if there's a theoretical requirement to perform the anova first.

Interesting discussion.

Actually, both examples you gave are very bad examples where multiple testing is not required or not sensible. More to that later. I will first comment on your question despite the examples you gave.

Salvatore made a good comment. If you are really interested in pairwise comparisons of multiple groups to one control, then Dunnett's test is often used. This test does two things: (i) it uses the pooled variance estimate from all groups and (ii) controls the family-wise error-rate.

An ANOVA is not at all required, as it answeres a question you don't ask. Unfortunately, some software offer Dunnett's test (and others) only in the context of an ANOVA (so you have to run some ANOVA first to select the tests). This is (usually) logically nonsense, as these tests are (usually) not logically linked to ANOVA. They only use the pooled variance estimate, and this is also calculated for the ANOVA. Because programmers are lazy, they let the software calculate this only in an ANOVA and use the calculated value for the tests. Therefore the software often required some ANOVA before offering these tests.

Using a pooled variance estimate for the test is a good thing, you should always do this where it is possible and sensible.

Controlling the family-wise error-rate is not always sensible. This is a complex issue and it depends on the research question and the experimental design.

To your examples:

Your first example actually needs only one single test, not multiple tests. The key question here is if the treatment-effect differs between the genotypes (i.e. does the altered gene interfere with the response to the treatment?). This is one (relatively) simple question and it should be addressed by one single test. The test is about the interaction of the two experimental factors "genotype" and "treatment".

Your second example likely does not need any test at all. Such experiments are usually done either to check the response for the low dose, using the high dose as a "positive control" (or to get an idea if the low-dose-response is already "maxed out"), or to indentify a dose at which the response is measurable or maximal. In the latter case the experimental design is poor. It would be far better to use several different drug concentrations and to do a proper dose-response analysis (a sort of regression analysis) what would give you better estimates of things like the dose at which the maximum response is obtained or who large the maximum response is. You would also be able to see how sensitive the response is to changes in the drug concentration.

Thank you very much for answering! I'll think about what you say! Bottom line is in these examples there is no need for Anova.

I think the bottom line is that when there are measurements for multiple groups, anova (or general-linear, generalized linear, or mixed models) are often used.

There is nothing compelling you to use one approach or another, with the caveat that some approaches are more appropriate than others.

Often it comes down to what question you are trying to answer.

Multiple t-tests are probably not the best approach in most cases.

That being said, don't be surprised if when you present something or try to get something published that someone tells you need to analyze things one way or another way.  That's just the way people are.