It's strange there are so many coastal routes. Shipping virtually anything by sea has been cheaper than moving it over land for a long time, and that probably includes troops. I would have expected roads to connect coastal settlements inland, not along the coast.
Going off of much later European experience, this depended on the type of traffic.
Despite the speed and cost/weight advantages of sea travel, the Habsburg Spanish empire maintained a land route between their possessions in Italy and the Netherlands [1]. Road travel had the advantage of reliability - more resistant to both natural disasters and to enemy action in war. This was very important for moving military forces through a large empire, which was a very important consideration for a polity like Rome which was constantly moving troops around to fight some revolt, war of expansion, or war of defense. There were also civilian applications - for small, expensive, non-time-sensitive cargoes.
In general, see [2] if you're interested in the transportation network of ancient time - see what combinations of weather, transport preferences (passenger carriage vs. donkey, for example, or safer daylight-only sailing vs. more efficient all-day sailing) push traffic onto coastal roads.
EDIT: For example, let's take the example of travel from Aelia Capitolina (Jerusalem) to Tyrus (Tyre/Sur). For a military application (travelling at military march speeds (60km/day) but restricting yourself to daylight sailing for fear of shipwrecks) relative travel speeds depend on weather - roads are better in winter, sea in summer. If you add in transfer time and cost (finding or rendezvousing with ships, cross-loading cargo, hiring porters) then the relative transfer times and costs change yet again.
In general, roads were better for: shorter trips, where transfer times and costs dominate; trips involving faster means of land travel, such as military forced marches, passenger travel by carriage, or in the extreme message passing by horse relay; and trips where protection from weather and enemy action (pirate or military) was paramount. Whereas bulk cargo of relatively low value, such as the massive grain shipments from Egypt to Rome, was only practical by sea.
The big other military advantage to roads is you may simply not have enough ships available to move the massive army you put together when you decide you've had just about enough of those pesky Gauls.
Settlements tended to concentrate along the cost and other water edges, for reasons of food availability, soil fertility, and access to the water base transport you mention. Existing local routes between them would have been used and upgraded as needed rather than building new links except where the time+capital expenditure made it worth while.
Settlements concentrated along the coast were mostly colonies of former naval powers, like Greek states, Phoenicians, and Carthage. These liked to settle close to shore but weren't connected by roads due to political reasons until submission to Rome.
It took hundreds of years for sea voyages at scale across the med to become a thing, as technology improved. The reach of the empire in this diagram is mostly due to Roman sea supremacy, but it was still difficult, expensive and prone to piracy/uppity city states.
Romans were notoriously poor sailors. Even when they acquired total domination over all sides of the Med (through sheer stubbornness and massive production of naval units, so that they could move enough land troops to the other side rather than trying to win naval battles), they couldn't completely eradicate piracy; this means sea routes were cheaper but not necessarily safer.
Also, I believe coastal routes were mostly connecting town to town in organic ways. An inland route was usually planned explicitly, and hence named for the consul or emperor who approved it, whereas it looks to me like the coastal routes took more topographical names (adriatica etc) or ended up as extensions of original inland routes (aurelia).
I understand that fighting piracy was a political problem. Pirates were mobile, and while any commander could suppress piracy in any area those not caught would move elsewhere and return when the commander's imperium was over and he had to return to Rome to give account.
It was feared that an admiral who was given an imperium for the whole of the Mediterranean would have such power that he would use it for political ands and upturn the system. So piracy grew with Roman hegemony, and when the seas had become so unsafe that the security of the grain supply was a political issue something had to be done. It turned out that the fears were well-founded, Pompeius was given his imperium maius over all the Mediterranean and 50 miles inland, he squashed piracy, and the First Triumvirate followed.
I'm off the impression that the Romans didn't travel by sea often, based on accounts of the cruising of the English channel; they seemed terrified of the sea. Not exactly sure why they didn't do this more often; maybe their strategy was to move by land and secure a spot channel as they went?
Sailing on the Mediterranean, which is very nearly an inland sea and has almost negligible tides, is an entirely different proposition from sailing on the Channel, which acts as a funnel for storms barrelling through from the Atlantic to the North Sea and vice versa. For an extreme example, see the Great Storm of 1987 [0], where winds reached hurricane force.
The Royal Yachting Association (UK governing body for all sailing sports) used to, and for all I know still does, regard the Med as inland waters, at least inasmuch as a dinghy-sailing instructor's certificate gained on the Med would not bear the coastal endorsement it would have had it been gained on the UK coast.
I don't know much about the Roman history, but a thought: There's a difference between crossing a sea and traveling on the sea skirting the coast (keeping the coastline always in sight).
Shipping large amounts of grain from Egypt was vital for the livelihood of the populace of Rome the city, so there was some maritime know-how in the empire.
Shipping was very much a commercial activity in the Roman Empire - you paid a ship owner for a spot. There were, however, pretty considerations pushing traffic to coastal roads - see my sibling comment.
