True. The shape can also matter. A coast naturally in form of a U can help protect ships from storms.
If the depth of the water was introduced, it could have other purposes, like how hard is it to extract oil.
The significance of the depth of a 'natural harbor' depends on the ship technology: a Trireme or Bronze Age galley with a draw of 6 feet that can turn around in just over its own length is a far cry from a modern oil tanker that needs a mile to turn around and draws 30 feet or more when loaded: the definition of 'natural harbor' will be very different in each case!
Several things would make coastal cities more important, or at least almost as important as they were historically:
1. A decent Trade system in the game. No more dual system in which your trade in Resources is magically independent of distance or technology.
2. A realistic Trade system. Bulk goods like Food cannot be traded any distance over land until you have railroads. Period. End of Discussion. You can get Production by trading things like obsidian, copper, bronze or iron tools (Obsidian for cutting edges was traded in the Pre-Game Neolithic, in fact) but you cannot trade enough food to make a difference to a city without sea or river - boat traffic - for the first half or more of the game. Even the recreated Bronze Age galleys could carry up to 20 tons at 10 - 15 kilometers per hour with a crew of less than 10. The best a cart or pack animal on land could do was 100 - 1000 pounds using 1 to 4 draft/pack animals at 3 - 5 kilometers per hour for less than half the day - and that's over good terrain or some kind of road. 1000 pounds of food, assuming it arrives unspoiled, will feed about 300 - 500 people for 1 day. A single trade galley would feed 10,000 + people for a day. There's just no comparison.
3. Harbors are built more than found, but they are built much, much earlier than the game has ever allowed. Some dates:
2570 BCE: Wadi-el-Jarf (modern name) in Egypt has the oldest known Port Structure, a 300 meters-long breakwater made of stone to protect anchorages.
1200 BCE: Phoenician cities on the Levant coast all building masonry breakwaters, piers and quays for harbors.
515 BCE: First evidence of cranes used (in construction of stone temples) - in Corinth, Greece, which also, by no accident, was a major trading port.
Also note that the first evidence for transporting troops and people by (coastal) sea is in pictorial form, from Egypt 2500 - 2300 BCE, so coastal sea movement should also occur much, much earlier in the game than has ever been allowed, and that would also increase the importance of coastal cities and the ability to exploit the coast for travel and access to resources.
4. Virtually all Harbor installations: breakwaters, quays, lighthouses, warehouses, etc. Increased the amount and value of trade through the harbor. Harbors were the object of as much production in facilities/infrastructure as any district in the city, and far more than any caravanserai or 'commercial district' for overland trade, but all the production resources put into harbors paid off and kept paying off as long as trade continued.
5. Sea Trade Routes are very resiliant. No amount of pirate activity ever 'destroyed' a Trade Route - simply made it go around or find an alternate route that was longer, less profitable, but still viable. Barbarian or other 'raids' on a naval trade route (or a land route, for that matter) should remove Value from the route every turn that they raid it, but it is destroyed only if one of the destinations at either end are completely blockaded/besieged or destroyed/captured.
6. Technology increases Trade Value on land and sea both. The Singularity-like change on land is the building of Railroads, which suddenly allow 1000s of tons to be carried for 100s of kilometers a day (just like on the sea) to any destination/city that has a rail connection. On the sea, open-ocean navigation and then Steam propulsion both change sea trade dramatically: making inter-continental trade possible, making trade more profitable because you can 'cut' distances through the open ocean, and making trade more reliable by removing reliance on wind direction and strength.
The other Singularity-like change to all trade has never been modeled in the game, and that is Containerization: the standardized Source to Destination containers that can be loaded and moved by truck, rail, air, or sea without disturbing the cargo. This resulted, between the late 1950s CE and the present day, in increasing all trade by an order of magnitude, decreasing loss during trade by almost as much, and speeding up the movement of all non-bulk cargo tremendously, which in turn resulted in modern 'just-in-time' delivery of resources to Factories and Populations and another massive increase in productivity and profitability
Get all those factors right, and the value of coastal cities will be where they should be.