Why this special treatment for mana-abilities? What are the design implications if they didn't go on the stack?
There are three reason I can think of:
Forcing arbitrary actions to be reversed
Consider this rule:
Players can obtain mana in the middle of casting a spell. If mana abilities used the stack, that means players would be able to cast spells in response. If the spell were to become unable to be cast, one would have to rewind all direct and indirect effects of those spells. Someone could have revealed private information, shuffled their library or lost the game as a result. How do you undo those?
Not only that, it would also make it far more likely for a spell to become unable to be cast, something that should never happen.
For example, consider this scenario where responding to mana abilities would be allowed.
Allowing spells that haven't been fully cast to be countered
The first step of casting a spell is to place it on the stack. A spell is a card on the stack (or a copy of spell), so it could be the legitimate target of a Cancel cast in response to activating mana abilities. That's just too complicated and messy to allow.
Plenty of other opportunities to react
Activating mana abilities is not something someone one normally does for its own sake. It's done as part of something else, such as casting a spell. Allowing this to be interrupted would be detrimental to the game flow and would add confusion. There are plenty of other points at which players can respond.
The earlier problems only surface when activating mana abilities when one would not have priority under the current rules. Could the game allow players to respond to the activation of mana abilities performed when a player has priority? Yes, but it would often be hard to distinguish whether an activation occurred before or during casting. It's far simpler to have mana abilities never use the stack rather that having the player try to figure out whether one can respond to a particular activation or not.
I think the simplest answer is that mana abilities are generally used while casting a spell to pay a cost. If they had to be put on the stack, then they could never be used while casting a spell because you would be taking another action before a previous action is complete.
If you follow 601.2 to it's conculsion you see that you could not activate the mana ability if it was not treated differently because you don't have priority while you are 'casting' a spell.
Yes you had priority when you started to cast the spell and you will have it again when you are done casting the spell, but while you are 'casting' it, (Paying its cost, choosing its targets etc) there is no passing of priority so no abilities or other spells can be used/cast.
So if it was treated like a normal ability, which you also can not activate while casting a spell, then you could never use them to pay a cost while casting a spell. they would always have to be used before you started paying the cost.
There is some history behind the decision. Back in the dark ages of MtG rules, before sixth edition, there were a lot of rules that were unintuitive and confusing. With the release of Fifth Edition, a new type of ability was introduced,
So, a Mana Source is anything that generated mana. Spells like Dark Ritual from earlier editions can be found with the card type Mana Source. Fifth Edition rules clarified that they may not be interrupted. This was necessary, because before the stack, Interrupts (depreciated, and later reclassified as Instants) were handled in batches
So, under the pre-fifth edition rules, you could kill a Llanowar Elves or Interdict a land tapping for mana to prevent a player from generating enough mana to play a spell, and the game would have to backup to the point of the illegal action of casting a spell you couldn't pay the cost for. Sixth Edition rules and the stack did away with all this confusion. There are no longer batches and special timing rules for Interrupts/Instants, they all go on the Stack. Abilities that generate mana don't go on the stack, amd therefore cannot be responded to, removing the necessity to specify on the cards that they cannot target mana abilities.