Would the Magna Carta have been better if it had guaranteed more rights to lower class people?
The obvious answer to this question is that it would certainly have been better for lower class people if this had been the case. Magna Carta was of course a very limited document by modern standards, granting certain rights to freemen (not serfs) and essentially making the English monarchy limited by the power of the barons. But we must understand the document in its cultural context. It was not a constitution in the sense that we imagine such a document today. Rather it was a feudal document that codified and reasserted many traditional obligations and limitations on the part of the monarch as a feudal lord. The barons had no notion of protecting common people, and indeed would not have even had a concept of "lower class" people. Neither would they have had a notion of universal rights that applied to all people. They understood society as a series of reciprocal connections, and Magna Carta was designed to ensure that the connections between king and barons remained reciprocal. This is not to say that Magna Carta had little effect. Some of its provisions were overturned by kings, parliaments and judges in the future, but many of its basic principles survived to be applied to kings and parliaments in very different contexts. Additionally (and in no small part due to the use of the word "freeman") in the document, it could be argued later, when social conditions were different, that Magna Carta could in fact be used to justify more protections for non-elites.