You couldn't do Synchronize Axis if Pills are of different Data Type.
The [Value (bin)] pill is an INTEGER, while the Value is FLOATING POINT --
a Number (Decimal) as defined in Tableau.
You can change a date type for the [Value] to a Number (Whole),
or use a calculation like INT( [Value] ) or even INT( ROUND( [Value] ) )
for the [Value] Dimension Pill in Columns to have the ability to Sync.
You can't do any changes to the Tableau-generated [Value (Bin)] Pill, though.
BTW, the problem has been solved
(the Sync behaviour has been changed)
in the recent versions of Tableau.
I don't know when it was fixed but when I tried it again in the new version - IT WORKED!!
Now, I'm stuck with the one remaining problem to adopt the bin sizes automatically. The bin sizes can be modified with parameter but I havent found a way to do it with code...
Glad it helped.
Regarding your 'remaining problem', the calculation could be written
that would have the same values as the Tableau-generated Bin pill.
INT( [Value] / [Parameters].[Bin Size] ) * [Parameters].[Bin Size]
Bin Size is usually a Parameter, but it could be a (Row-Level) Calc as well.