Independent evidence for the classification of topological 4-manifolds? Is there any evidence for the classification of topological 4-manifolds, aside from Freedman's 1982 paper "The topology of four-dimensional manifolds", Journal of Differential Geometry 17(3) 357–453? The argument there is extraordinarily complicated and a simpler proof would be desirable.
Is there evidence from any other source that would suggest that topological 4-manifolds are so much simpler than smooth 4-manifolds, or does it all hinge on Freedman's proof that Casson handles are homeomorphic to standard handles?
My question is motivated from a number of points of view:


*

*The classification of topological 4-manifolds is now 30 years old and an easier version of the proof has not emerged. In contrast, Donaldson's invariants have been superseded by more easily computed invariants. This is a very unsatisfactory state of affairs for such a far-reaching topological result, particularly as it is so regularly used in proof-by-contradiction arguments against results in smooth 4-manifold theory. 

*As the Bing topologists familiar with these arguments retire, the hopes of reproducing the details of the proof are fading, and with it, the insight that such a spectacular proof affords. I am delighted to see that the MPIM, Bonn is running a special semester on this topic next year. Hopefully this will introduce these techniques to a new generation of mathematicians (and save them from having to reinvent them!)

*It may be possible to refine the proof to gain more control over the resulting infinite towers - and perhaps get Hoelder maps rather than homeomorphisms, for example. This would require either a better exposition of the fundamental result or some new independent insight, which was the basis of my question.
 A: The answer to this question might have changed since it was first asked nine years ago: a book is now available whose goal it is to give a detailed elaboration on Freedman's work:
The Disc Embedding Theorem, ed. Behrens, Kalmar, Kim, Powell, Ray (Oxford University Press, 2021).
Some excerpts from the Preface:

We choose to follow the proof from [FQ90], using gropes, which differs in many respects from Freedman's original proof using Casson towers [Fre82a]. The infinite construction using gropes, which we call a skyscraper, simplifies several key steps of the proof, and the known extensions of the theory to the non-simply connected case rely on this approach. …

We briefly indicate, for the experts, the salient differences between the proof given in this book and that given in [FQ90]. First, there is a slight change in the definition of towers (and therefore of skyscrapers). …

Additionally, the statement of the disc embedding theorem in [FQ90] asserts that immersed discs, under certain conditions including the existence of framed, algebraically transverse spheres, may be replaced by flat embedded discs with the same boundary and geometrically transverse spheres. The proofs given in [Fre82a, FQ90] produce the embedded discs but not the geometrically transverse spheres. We remedy this omission by modifying the start of the proof given in [FQ90], as in [PRT20]. … Besides these points, the proof of the disc embedding theorem given in this book only differs from that in [FQ90] in the increased amount of detail and number of illustrations.

In Section 1.5 they mention some things that are not covered in the book. In addition to bypassing the part of Freedman's original proof that "consisted of embedding uncountably many compactified Casson handles within the original Casson handle and then applying techniques of decomposition space theory and Kirby calculus," they say:

Note that the ambient manifold is required to be smooth in the statement of the disc embedding theorem. There exists a category preserving version of the theorem, where ‘immersed’ discs in a topological manifold are promoted to embedded ones. However, the proof requires the notion of topological transversality and smoothing away from a point (see Section 1.6). These facts, established by Quinn, in turn depend upon the disc embedding theorem in a smooth 4-manifold stated above. The fully topological version of the disc embedding theorem is beyond the scope of this book, since we will not discuss Quinn's proof of transversality.

A: After 7 months, over 800 MO views and (as suggested) emails to experts, the answer to the question is "No": other than Freedman's 1982 paper, there is no evidence what-so-ever that topological 4-manifolds are so much simpler (i.e. determined up to homeomorphism by their intersection form) than smooth 4-manifolds. Subsequent research (capped gropes etc) hinge on the key step in the paper - the removal of "gaps" in the "design". While this is a highly unsatisfactory state of affairs for the reasons mentioned in the original question, it is what it is.
A: There's a somewhat different exposition in Freedman and Quinn's book. I think
the main difference is that they use gropes instead of Casson handles. Gropes are
made of embedded surfaces instead of singular disks, and introduce some technical
simplifications to the proof (they originated with Stan'ko). 
Richard Stong gave a correction to one of the arguments in the book, although
I think it isn't relevant to the proof of the disk theorem.  
A: There is no other evidence. In fact there is absolutely no evidence what so ever. I have never met a mathematician who could convince me that he or she understood Freedman`s proof. I attempted to read that monstrosity of a paper a number of times by myself and quite a few times with a group of other mathematicians. We never were able to finish checking all  of the details. Such seminars always ended before we could make it through even half of his paper. No other expositions on the subject seem to be any better. It is truely an odd state of affairs that after all of these years no one has managed to write a clear exposition of this so called proof,and that no one seems to question the claim that there ever was a proof. I remember thinking as a young mathematician either this "proof" is sheer nonsense or someone will eventually write out a clear and detailed explanation. As of April of 2011 I have understood that the so called proof is full of errors and they can not be fixed. I mentioned this to several mathematicians during the summer of 2011 and I believe these conversations are directly linked to the dialogue seen here on math overflow.
A: Maybe these notes (entitled "THE 4 DIMENSIONAL POINCARÉ CONJECTURE") of Danny Calegari are useful for your interests?: https://math.uchicago.edu/~dannyc/courses/poincare_2018/4d_poincare_conjecture_notes.pdf
