Practicality of using different types of battery cells to avoid DC-to-DC conversion
Every battery chemistry has it's own charge / voltage curve, it's own internal resistance, and it's own aging characteristics.
This means that even if you solved the charging issue and sized the cells to give the same nominal capacity (which wouldn't just be a case of making them all the same size, it would depend on the nominal current draws of each voltage rail) you would still have fluctuating relative differences in your voltage rails depending on current draw on each rail and battery charge level.

All of those are fixable with a simple LDO on each output.
But a battery voltage can easily change by at least 30% between full and empty. That means that assuming you want a constant voltage over the full charge range your average LDO efficiency is going to be under 85% for a perfect, 0 drop out device. That's well within the range of a good DC-DC switcher.

So your power supply is simpler but about the same efficiency.
Your charger is now far more complex and non-standard, easily adding more complexity than you saved in the power supply.
And you've replaced your nice standard battery for an application specific custom battery that costs vastly more.