Replacing Geographical-Categorical Variables with Geographical-Continuous Variables? Suppose I have a dataset in which I am trying to model "asthma prevalence" using explanatory variables such as "age", "profession" and "geographical location" using a regression model. Currently, I have the "geographical location" variable as a categorical variable (e.g. the City code in which each person lives).
 id profession   city gender age   salary asthma
1  1    student City A      M  23 41648.96    YES
2  2    student City B      F  27 23863.39     NO
3  3   engineer City A      F  29 36141.04     NO
4  4 contractor City C      M  34 41432.74     NO
5  5    student City A      F  29 33897.44    YES

Imagine I have access to the full address where each person in this dataset lives - this means that in theory,  I have the ability to convert this "geographical categorical" variable into two "geographical continuous" variables, i.e. longitude and latitude. The dataset would look something like this:
  id profession   city Longitude Latitude gender age   salary asthma
1  1    student City A -75.10793 44.92730      M  23 41648.96    YES
2  2    student City B -75.16746 44.41723      F  27 23863.39     NO
3  3   engineer City A -75.54285 44.59074      F  29 36141.04     NO
4  4 contractor City C -75.04271 45.34247      M  34 41432.74     NO
5  5    student City A -74.46469 44.83997      F  29 33897.44    YES

This leads me to my question - in general, could the argument be made that it is likely more beneficial to convert this "geographical categorical" variable into "geographical continuous variables"?
This is the following argument that comes to mind: Within the same City, it is not unreasonable to believe that similar types of people with similar asthma prevalence rates may live closer to one another compared to people with different types of characteristics (e.g. poor areas vs. rich areas - people in poorer areas might be likely to smoke more, work in factories ... all factors that may contribute to asthma). Only using the City - the regression model would likely miss out on these within pattern cities (e.g. https://ichef.bbci.co.uk/news/976/cpsprodpb/59C4/production/_103108922_mdrum_rich_meets_poor-10.jpg.webp).
Thus - could this be considered a valid approach - converting "geographical categorical variables" into "geographical continuous variables"?
At the moment, the only disadvantage I can see are complications relating to statistical inference. For example, suppose I built a Logistic Regression and I had wanted to calculate the Odds Ratio which showed the difference in asthma for residents in City A vs. City B. If the geographical categorical variable were to be made continuous - as I understand, you would now be forced to compare the change in odds for developing asthma "per unit change in degree longitude", and the interpretation of this might be less intuitive compared to the City level interpretation. However, I think it might be possible to still use longitude/latitudes and account for individual cities at the aggregate level by using a "Nested Mixed Effects Model" (e.g. the model assigns a Random Effect to each city) - this seems like the "best of both worlds": the regression model has the ability to benefit from the information contained with the granularities longitude and latitude, and standard inference tasks such as the Odds Ratio can still be calculated and interpreted in the standard sense. But then again - I am not sure if what I just described could be considered as "Statistical Double Dipping" and add unwanted noise/effects such as multicollinearity.
Can someone please comment on this?

I don't think you have to worry about collinearity when including both cities and coordinates unless you are doing something complex with the coordinates or have very few cities. Whether you should include cities as random effects can hopefully be answered by Ben Bolkers fantastic glmmFAQ: https://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#should-i-treat-factor-xxx-as-fixed-or-random
I'm assuming that you probably don't have enough data to get a solid estimation of the geographic asthma prevalence within each city, but you could construct a model with spatial correlation. This means that the correlation between 2 observation within a city falls with their distance. Again Ben Bolkers FAQ gives you good start on that:
https://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#spatial-and-temporal-correlation-models-heteroscedasticity-r-side-models
