Restating the problem
The traditional interpretation is well-known that Moses struck the rock rather than speaking to it. The OP himself is well aware of this tradition but is hesitant to accept, because the offense seems too petty to warrant such a harsh punishment. Why make a big deal of how the water is being produced? God asked Moses to perform a miracle in front of the Israelite crowd in order to sanctify His name (this is evident from v. 12), and it seems like this was achieved by Moses’ striking just as much as it would have been through him speaking. So why punish him for this.
Furthermore, v. 12 makes it clear that Moses’ offense was his lack of belief/trust in Yahweh. However according to the traditional approach this can hardly be considered a lack of trust. It would be more appropriate to call it an act of disobedience, but why talk about lack of trust in Yahweh when Moses performed the miracle of hitting the rock in front of their eyes trusting in Yahweh that He will bring forth water from a lifeless rock!
Traditional interpretation vs. others
We may be tempted to just discredit the traditional interpretation and move on to some other more satisfying explanation. But mush to our dismay there are no better explanations. Most of the alternative interpretations are not supported from the text but require some imagination on the readers part, and they rest on speculation and theory rather than on solid hermeneutical grounds. One needs to look no further than Nahmanides’ commentary where the author brings no less than ten different interpretations of the sin of Meribah, only to discount them all. The traditional approach on the other hand is readily apparent to the reader and requires no imagination from the reader and is thus hermeneutically superior to others. That is why I choose to stick with this interpretation. But at the same time there is no denying that there are some serious philosophical problems with this approach, which makes it a bit unappealing to the modern scholar. I myself have been grappling with this problem many years, I read it and reread it many times in the hope that I will find something that I have missed, alas there was nothing to be found. Eventually I resigned and concluded that the answer must lie in the traditional approach as it seemed the most natural reading.
Striking the Rock: Miracle or Natural Phenomenon
To solve this biblical riddle I want to suggest that the author in Num. 20 did not perceive striking the rock as a supernatural act but rather as mundane act of digging. The image of Moses striking a rock with his rod miraculously causing the inanimate rock to bring forth water is so deeply ingrained in our psyche that we take it for granted but its not necessarily how the author in Num. 20 viewed it. According to Issar, Bedouins of southern Sinai dig into crystalline rocks to find wells, and it is not far fetched that Moses engaged in similar practice of digging and chipping away at the limestone with his rod to find a well. Once the wall of an aquifer has been penetrated, gravity would compel the water to rush through rocks and cracks to fill up the newly created basin with water giving the appearance of the rocks giving forth its water, hence the terminology of "stike the rock and water shall spring from it" (Exodus 11:6). According to another source, Bedouins actually dug their wells with pointed sticks. It is quite remarkable that Numbers 21:18 also describes the practice of chieftains digging wells with their staffs and rods,
It's the well that the leaders dug, the one carved out by the nobles
of the people with their scepters and staffs. (ISV).
The fact that striking instead of digging is used in v. 11 must not deter us, for a striking motion may have been used to crack open dried up rocks and reveal the water underneath. Thus hitting or striking the rock may have seemed the most natural way to describe Moses’ actions. (I am not saying that the biblical authors understood exactly how this process worked, only that they were aware that it was something natural).
If we are right in supposing that this is how it has been originally understood, then I think we may better understand where Moses went wrong here. God specifically told Moses to speak to the rock and not to strike it, because he wanted to teach the Israelites a lesson that nothing is beyond His reach and that they should stop doubting His power. Here the Lord wanted to demonstrate His power by having Moses speak to the rock and command it to give forth water, they in turn would be dumbstruck by this miraculous act and an essential lesson would be learnt. Instead Moses went and dug through the rock to find a well. Perhaps Moses lost himself in an act of desperation, whatever it was Moses demonstrated a lack of trust in God’s word; in a moment of haste Moses doubted God’s ability to perform miracles thereby failing to sanctify God’s name.
In fact, this is not the first time Moses doubted God’s ability to provide for his people, see for example Num. 11:21-24 where Moses demonstrates a lack of faith in the Lord. Here too Moses lost himself and questioned God’s ability to perform miracles, except this time he didn't get away with it and rightfully deserved his punishment of not being able to enter the land of Canaan.
It should be noted though that there are some biblical passages in which the act of splitting rocks clearly have miraculous connotations. In some places (Psalm 114:8) it is even likened to the splitting of the Red Sea and the eating of the manna (Deut. 8:15), acts of wonders which are clearly perceived as miraculous phenomena by the biblical authors. I am merely suggesting that the author of Num. 20 may have viewed it differently.
And contrary to some bible scholars who believe that the Rock narrative in Exodus 17 stands in direct opposition to Num. 20 I think that they actually complement each other. Exodus 17 sheds light on Moses’ actions here to strike the rock rather than speak to it. Moses may have relied on previous experience where he struck the rock and it yielded water. Moses was using the same method he was taught previously by God himself. Only this time God had other plans.