The generic tendency in naval history has been that deeper ports are better as they allow larger ships to dock at the port. The importance of deeper water ports increased rapidly in the 19th century when ship designed started to incorporate steel and to build larger draught vessels—this development has, in a way, carried on up to now. There is one instance which I've found where a shallow-water port was desirable (below). Are there other examples of naval bases being deliberately situated in shallow-water harbours post-1801?
The one example I know about involved disregarding Darwin as a potential submarine base in favour of Tjilatjap:
Yet the depth of water could be accounted a disability. One of the reasons (given by the American submarine force commander) for withdrawing the tenders from Darwin to Tjilatjap was that if they were sunk by air attack in Darwin harbour the depth was such that it would not be possible to raise them.
—Hermon, 'Volume I – Royal Australian Navy, 1939–1942'
In general, an example of a shallow port being a limitation:
Catherine the Great had planned a relatively ice-free naval base and port at Baltic Port, now Paldiski, west of Revel, but it had proved too shallow and contemporary technology was not up to dredging it.
—Greenhill, 'The British assault on Finland, 1854-1855'
The definition of "deep" vs "shallow" is a tough one. Modern specifics note that 10m is the lower boundary for "deep". The question's focus is on history, however, and I don't think the same applies. Overall, for the arguments to count there should be contemporary evidence from the decision-makers that describe the relative benefits of the military port with regards to its depth, with depth the primary consideration.
Modernising existing older military establishments also doesn't count. In many cases, countries had to get by with what they had access to and the shallow-water harbours were the only available ones. For example, the development of Wilhelmshaven sees gradual dredging to accommodate the increasing cruisers and battleships in the late 19th and early 20th century. Yet, the Germans didn't have (as far as I know) a deep-water harbour that would have been open to the North Sea.