Why is dropout favoured compared to reducing the number of units in hidden layers? Why is dropout favored compared to reducing the number of units in hidden layers for the convolutional networks?

If a large set of units leads to overfitting and dropping out "averages" the response units, why not just suppress units?

I have read different questions and answers on the dropout topic including these interesting ones, What is the &quot;dropout&quot; technique? and this other Should I remove the units of a neural network or increase dropout?, but did not get the proper answer to my question.

By the way, it is weird that this publication A Simple Way to Prevent Neural Networks from Overfitting (2014), Nitish Srivastava et al., is cited as being the first on the subject. I have just read one that is from 2012:
Improving neural networks by preventing co-adaptation of feature detectors.
Dropout only ignores a portion of units during a single training batch update.  Each training batch will use a different combination of units which gives them the best chance of that portion of them working together to generalize. Note the weights for each unit are kept and will be updated during the next batch in which that unit is selected. During inference, yes, all units are used (with a factor applied to activation...the same factor that defines the fraction used)...this becomes essentially an ensemble of all the different combinations of units that were used.
Contrasted with fewer units, the fewer units approach will only learn what those fewer units can be optimized for.  Think of dropout as an ensemble of layers of fewer units.(with the exception that there are partial weight sharing between the layers)