Is there a machine learning model suited well for longitudinal data?
Assuming we are not talking about a time series and also assuming unseen data you want to make a prediction on could include individuals not currently present in your data set, your best bet is to restructure your data first.

What you want to do is predict daily outcome Y from X1...Xn predictors which I understand to be measurements taken. A normal approach here would be to fit a RandomForest or boosting model which, yes would be based on a logistical regressor.

However you point out that simply assuming each case is independent is incorrect because outcomes are highly dependent on the individual measured. If this is the case then we need to add the attributes describing the individual as additional predictors.

So this:

id | day | measurement1 | measurement2 | ... | outcome
A  | Mon | 1            | 0            | 1   | 1
B  | Mon | 0            | 1            | 0   | 0


becomes this:

id | age | gender | day | measurement1 | measurement2 | ... | outcome
A  | 34  | male   | Mon | 1            | 0            | 1   | 1
B  | 28  | female | Mon | 0            | 1            | 0   | 0


By including the attributes of each individual we can use each daily measurement as a single case in training the model because we assume that the correlation between the intraindividual outcomes can be explained by the attributes (i.e. individuals with similar age, gender, other attributes that are domain appropriate should have the same outcome bias).

If you do not have any attributes about the individuals besides their measurements then you can also safely ignore those because your model will have to predict an outcome on unseen data without knowing anything about the individual. That the prediction could be improved because we know individuals bias the outcome does not matter because the data simply isn't there.

You have to understand that prediction tasks are different than other statistical work, the only thing we care about is the properly validated performance of the prediction model. If you can get a model that is good enough by ignoring individuals than you are a-okay and if your model sucks you need more data.

If on the other hand you only want to predict outcomes for individuals ALREADY IN YOUR TRAINING SET the problem becomes even easier to solve. Simply add the individual identifier as a predictor variable.

To sum it up, unless you have a time series, you should be okay to use any ML classification model like RandomForest or boosting models even if they are based on normal logistical regressions. However you might have to restructure your data a bit.