Take it from someone who works in the field. It is not old, nor has it been disproven. In any case, let’s go through what you have to say…
You need to talk about what scales. The Big Bang theory predicts homogeneity at the largest scales. Current all-sky surveys indicate such homogeneity exists. In effect, despite the fact there are local over-densities (clusters) and under-densities (voids), in the end these occur with a regularity that is uniform over a large scale.
Think about spilling a bag of marbles over the floor. In one sense the distribution of marbles is uniform (homogeneous). In another sense, it is clumpy (you will see clumps of marbles here and there and places without marbles as well). The statistics of these distributions are of great importance to modern cosmology.
Moreover, things with mass attract each other (that’s called gravity), so stuff we see tends to be corrollated with other things we see. This is where the “clumpiness” comes into play.
All of this was known back when the model was predicted. All of this was demanded of the model in order for it to work. The Big Bang model was said to HAVE to exhibit homogeneity on large scales while allowing for the clumpiness on small scales.
This is exactly what scientists observe.
Again, you have to say on what scale. On small scales the Big Bang model necessarily predicts the opposite (galaxy-galaxy correlation).
And this is EXACTLY what we see, if you go out to large enough scales!
Indeed this all depends upon what your definition of “large” is. If on the scale of the universe, then no, you would not expect to see it. However, we have two large structures that are clumpy “clusters” and “voids” These two tend to exist in statistical modelling described above. When we put the initial conditions in, determined mostly by the anisotropy in the CMB we see that we can model the voids and cluster correllations very well from simple physical principles. This is the wonder of what the Big Bang model has brought us. Not only does it predict large scale homogeneity which we see, it even accounts for the variability (or clumpiness, as you put it) we also see. In short it does what you claim it doesn’t do.
Ah! The old supercluster conundrum. What makes structures that are too large too be virial over the time-scale of the universe? The answer is found in CMB evidence of inflation. When you have quantum fluctuations in your seed, you end up enlarging this to the scales we see today. CMB anisotropies are seen to be exactly what is necessary to explain these structures.
In short, the “clumpy” universe is well predicted and allowed for by the Big Bang model. It was a noble effort at falsification, but I have to say, try again!