There's nothing wrong with reinforced concrete, but the incentives to produce long lasting buildings are not there. The cheapest bidder will generally win and their building will last the "design life" of the building, but often not much more. The simplest way to change this is to extend the design life, which would result in stainless steels or another more expensive material being used in this application.
Or if it's made of stone. Stacking giant stones on top of each other is a sure-fire way to make a building outlive you.
After that, the longest-lived buildings that I am aware of are made of wood. The catch is they've been rebuilt 50 times, once per time they burned to the ground.
After those, the longest-lived buildings are made of Roman concrete that we can't reproduce. (To give you an idea how insane Roman concrete was, you can go kayaking north of Naples, and kayak through a concrete Roman building that is sitting on piles in the Mediterranean sea)
The bigger difference in components is the kind of cement the Romans (and we "moderns" until a few years ago) used, i.e. pozzolanic cement, nowadays everything is "portland" cement.
BUT the definite difference is the kind of structures, Romans did not use "reinforced" concrete, only various types of "plain, non-reinforced" concrete, and all their structures are based on the main characteristic of concrete, which is its resistance to compression.
The idea of reinforced concrete is all about adding to a material with excellent compression resistance (but no resistance on tension/traction) a material (steel) with excellent resistance to tension/traction and relatively poor (in the quantities used in reinforced concrete) resistance to compression, obtainining a composite material that excels in both.
About ashes, overall it is more about their size that about their nature, concrete is a composite and if you have all possible sizes of aggregates (ashes are very, very small sized particles) in the "right" amount you essentially fit "better" the space, i.e. you have a higher density of the resulting composite, and, particularly when compression resistance is the goal, the higher the density the better the resistance.
Imagine (say) that you have to fill a 100x100x100 mm box with 10 mm balls, you can fit in them a certain amount of these balls (roughly 10x10x10=1000), but you are leaving lots of "air" between them, a single 10 mm ball is 2/3x3.1416x5^3=262 mm3, so the 1000 balls total 262,000, but the volume of the box is 100x100x100= 1,000,000, now if you have some 2 mm balls you can add them in the same volume, and then if you have some 0.5 mm balls you can put some of them in that same box as well, etc.