Would there be any reason to bore a tunnel entirely through a world?
I can think of one reason and it's the same as why the chicken crossed the road - to get to the other side. ;)
So, why then would someone want to use a hole instead of surface transport like you suggest?
1) It's cheaper
2) It's more reliable
3) It's more 'eco-friendly'
4) It's faster
I could go on.
Before going further we need to clarify some apparent assumptions.
You seem to be comparing "a world" with our world. The primary reason I suggest this is because you suggest there is heat at the core - not all planets have hot cores.
...surface transport would be easier.
What kind of technological, environmental or chemical environment might force
a society to decide to go through rather than around a planet?
What if "a world" had a mountain range around the equator which was too high to get over easily (even with an airplane)?
What if "a world" was nothing but a mucky swamp, or a sandy desert, or an accordion of mountains that never ended? Again, assuming no airplanes. One does not need as much technology to dig a hole if a hot core is not an issue.
And those are just a few geological hazards. We could also talk about wind patterns that made the equator a 'hot zone' from natural or man made radiation. What about a group of people, animals, insects, ... that make it nearly impossible (or at least extremely hard) to traverse from one side of the globe to the other.
There are many scenarios one can imagine that makes it hard to get from one side of a world to another.
Lastly, as other have noted, gravity is the main force providing the 'work' to get from one side of the planet to the other so once the hole was 'built' transportation costs could be minimal. If friction-less the object would emerge to the same height above the ground as it was dropped. Since a friction-less system of any kind is very difficult one could easily use electromagnets, tethers or other simple means to bring the payload whatever extra distance to the surface was required due to the losses from friction.