Your issue is not with one-tile distant cities but with "useless" cities. I've seen a handful myself. I think the solution is to work on game mechanics to reflect their real life utility rather than having sparsely populated super-cities.
Regarding Arguim, one mechanic I would like to see added is an overhaul of navies. Power in the period of imperialism was safeguarded by navies and navies were supplied by ports. [...]
I think trade resources are currently very well represented by this mod, however trade mechanics could use overhaul when possible.
I agree in principle, not sure about the details of your specific suggestions though.
An easy but heavy-handed solution could be to substantially increase unit supply costs.
To make tightly packed cities more valuable, how about several cities can share a given resource if they are only one tile apart? I.e. for the purposes of limited resource supply they all count as one city, not several. To illustrate, let me take Zaddy's screenshot here:
First, assume Alexandria belongs to Egypt too. Second, let's pretend Egypt actually has two Wheat resources connected to its trade network. Third, if that isn't already the case, let's say a single Wheat resource can only supply a single city.
With my mechanic there would basically be three "clusters" of cities that the limited resource supply mechanic would consider to be a single city each instead of several. Currently, two Wheats would only supply e.g. Nwt-Rst and Alexandria. What I'm suggesting is that here those same two Wheats would instead supply the three cities on the Mediterranean coast as well as the Nwt-Rst, Abw and Akhetaten triangle, assuming neither Selima nor Mut have a decent amount of culture. Instead of 8 cities the resource assignment algorithm would only see 3 here, so only one "city" (actually a group of two cities in this example) would go without Wheat instead of 6.
If that's too contrived or complicated to code, we could just use distance maintenance as a shorthand instead, so all cities whose distance maintenance cost is below a certain threshold (let's say 0.5) would share the resources of the capital or the nearest city with an Administrative Center.
If we look at that Egyptian screenshot again as an example, I would imagine it like this: In the beginning only Akhetaten and Abw would share Nwt-Rst's resources. With jails in place, Pi-Ramesses and Mut could be supplied from the capital too. Finally, if Egypt even lives that long with this setup, Alexandria would join the party when it completes a Courthouse. That is to say, the radius around a Palace or Administrative Center within which any cities would be supplied with that city's resources for free would be 2 tiles at first (so only within the BFC), then 3 tiles with Jails, and finally 4 tiles with Courthouses on top of that.
Specifically I was referring previously to Akhetaten, which captures no resources not already captured by a previous city and works no valuable unworked tiles.
Akhetaten is a port which should pay for itself with the Great Lighthouse and can work two good tiles.
Other notable offenders include Mut and the city to the west of Alexandria, who also capture no new resources or valuable unworked tiles and have to take other tiles from already productive cities just to do anything at all.
The city west of Alexandria puts additional culture pressure on the Spartan Fish, and again pays for itself with the Great Lighthouse.
Selima technically captures the cotton but is also of very dubious utility.
Selima is doing fine.
If you'd founded these cities in vanilla Civ4, any high level player would rightly call that a poor move for a variety of reasons, and the reasons it's a poor move are made even more prominent by DOC's ruleset.
IIRC high level vanilla Civ4 players are all about cottage sharing in the early game to get a rich Bureaucracy capital up and running. The unhealth from the flood plains punishes cities that grow too big, making it more attractive to have several small cities instead of few large ones.