Has there been an answer to why there is no non-combat Experience points awarded in D&D 5e? I'm not referring to XP gained from monsters by defeating them other than combat, but XP awarded for completing quests, roleplaying, or other non-combat activities. I'd prefer an answer quoted from Mike Mearls or Jeremy Crawford if possible.
The premise of your question is flawed because the system allows for non-combat XP.
Your question assumes that there is no non-combat XP in 5e, but this is not true. The DMG (pg 261) leaves the door open for awarding noncombat XP:
You decide whether to award experience to characters for overcoming challenges outside combat. If the adventurers complete a tense negotiation with a baron, forge a trade agreement with a clan of surly dwarves, or successfully navigate the Chasm of Doom, you might decide that they deserve an XP reward.
In fact, the same page gives specific guidelines for how much XP to award (emphasis added):
You can also award XP when characters complete significant milestones. When preparing your adventure, designate certain events or challenges as milestones, as with the following examples: ...
When awarding XP, treat a major milestone as a hard encounter and a minor milestone as an easy encounter.
Jeremy Crawford backs this up in an interview:
MT: I’ve noticed there’s more opportunities to talk and formally tie experience points to negotiating with enemies instead of killing them. It does make DMs have to think about advancement. Tyranny of Dragons has rules of leveling between sessions, which is definitely a new mindset that’s different from “killing one more orc to get exp.”
JC: The advantage of this open-ended approach is that if the DM prefers to track experience points, the DM can do that because since things are more open-ended the DM has more space to play in, so if the DM would rather have more traditional combat encounters and those are the source of experience points, that can totally be done.
In a tweet, Crawford has said that he does not tie XP to combat in his home game:
In my home game, I award XP when it feels right for the story. Sometimes I just say, "You gain a level." #DnD #wotcstaff
In a tweet, Mike Mearls has said:
@RobertPascuttin the system really shouldn't use XP as a measure - it muddies the issue of its meaning.
I'm not sure exactly what he means here, but it does seem to be something against the idea of XP being a strict measure.
Thus, we can see that the designers have left lots of space in the system for the DM to award non-combat XP.