absolutely nothing , but then you may for example decide to use search engine friendly URL's eg
page.php?var1=var1&var2=var2 .... etc
now you have to recode all of your paths as the links now requires an extra '../' or two (or 3)
now thats just 1 example which happens to fit my preference
however coding absolute paths and then abstracting those puts you in a position where you simply can not lose.
I would say that 50-60% of my day to day work now reuses existing code , especially for generic frameworks of sites/applications , at this point simple steps such as MeGa suggests can reap massive benefits , the more complex the applications get , the more sense it makes.
The ONLY downside to the above is the extra parsing that PHP has to do , and that would be a fair argument on its own , but firstly the overhead is minor , however if you are an efficiency freak (like me) then you negate that overhead with cacheing , be that administrative or at runtime.
The point I am trying to make is that the method noted is not useless , again , far from it and it should not be dismissed without thought.