BUG: concat with sparse not propogating default_fill_value

[jreback]

from #12174 (comment)

In [1]: df = pd.SparseDataFrame(np.random.choice([0., 1.], size=(5,5)), default_fill_value=0.)
   ...: 

In [2]: df
Out[2]: 
     0    1    2    3    4
0  0.0  1.0  1.0  0.0  0.0
1  1.0  1.0  1.0  0.0  1.0
2  0.0  1.0  0.0  1.0  0.0
3  1.0  1.0  1.0  0.0  1.0
4  1.0  0.0  0.0  1.0  1.0

In [3]: df.default_fill_value
Out[3]: 0.0

In [4]: pd.concat((df, df), axis=1)
Out[4]: 
     0    1    2    3    4    0    1    2    3    4
0  0.0  1.0  1.0  0.0  0.0  0.0  1.0  1.0  0.0  0.0
1  1.0  1.0  1.0  0.0  1.0  1.0  1.0  1.0  0.0  1.0
2  0.0  1.0  0.0  1.0  0.0  0.0  1.0  0.0  1.0  0.0
3  1.0  1.0  1.0  0.0  1.0  1.0  1.0  1.0  0.0  1.0
4  1.0  0.0  0.0  1.0  1.0  1.0  0.0  0.0  1.0  1.0

In [5]: pd.concat((df, df), axis=1).default_fill_value
Out[5]: nan

[jreback]

cc @mdgoldberg if you'd like to take a stab at this.

[hexgnu]

So I took a somewhat stab at this.

the problem here is that BlockManager strips out default_fill_value. I started going down the road of adding in SparseBlockManager, but it felt really hamfisted to me and introduced a bunch of new branches in the code.

Also I know from other discussions #19239 that this might be a waste of time.

Thoughts @jreback, or @TomAugspurger ?