[RPG] Do experience points in 5e continue to stack or do they get expended and leave carry over points towards the next level

First, I don't believe that "why" is something that this community can answer; this was a decision of the designers and their reasons, to the extent that they have any, are a mystery.

Notwithstanding, your question is why the XP per level looks like this:

Steady growth until 11th level, then a sharp drop and not reaching the 10->11 level again until 14->15.

However, the XP values are only one side of the equation; the other is how much XP is gained per encounter (p.82 DMG). Ignoring modifiers, by combining these you get this chart:

Easy, Hard and Deadly encounters are approximately 2/3, 1.5 and 3 times a Medium encounter (presumably because of rounding off). Focusing just on the "Medium" encounters (which should be the bulk of encounters) it can be seen that you need 6 to reach levels 2 and 3, 12 to reach 4, approximately 15 for levels 5 through 10, 17 for level 11 and then about 9 to 10 for levels 12 to 20.

However, due to the strange way that XP budgets do not equate with XP awarded, you will only have this number of encounters if every encounter is with a single monster. If your encounters are typically with 3-6 creatures (most of mine are) then you will need twice as many encounters to get the same number of XP.

In this context, the jump at level 11 is only about 10% and then it falls to a much lower and approximately constant value.

If I were to speculate, and I will, I would guess that the design intent is to:

• Provide relatively rapid advancement through the early levels.
• Slow down this advancement in the mid-levels (4-11) to an approximately constant level of about 15 medium/10 hard encounters (noting that difficulty factors will make the actual number of encounters 2-3 times this).
• Provide more rapid advancement (about 1/3 quicker) for the levels 12-20.

This accelerates the PCs through the fragile early stages and provides rapid gratification, provides a long period of play in the mid-levels, suitable for the dungeon-grind and then move more quickly through the levels where nation and world shaking events may be happening.

Feats, generally, aren't supplanted by beast statistics. (Though your ability to make use of them may be supplanted.) Alert and Lucky, specifically, still apply in their entirety.

Your game statistics are replaced by the statistics of the beast. (PHB p.67)

To see what is supplanted or augmented, take a look at beasts' statistics. ("Statistic," as a defined term, appears on MM pp.6-11):

1. Size. Your size is replaced by that of the beast.
2. Type. Your type is now beast, not humanoid.
3. Alignment. Not replaced, per Wild Shape.
4. Armor Class. Replaced.
5. Hit Points. Replaced. So no "Tough" carryover, per both our site and Sage Advice.
6. Speed. Replaced.
7. Ability Scores. STR, DEX, CON replaced. INT, WIS, CHA not, per Wild Shape. (We'll get to initiative and Alert in a moment.)
8. Saving Throws. You retain your proficiencies and choose the higher ability modifier of yours and the beast form's, per Wild Shape.
9. Skills. Ditto saving throws.
10. Vulnerabilities, Resistances, and Immunities. You've got 'em.
11. Senses. Replaced. (Specifically called out: if your humanoid form has darkvision and the beast form doesn't, you've just lost darkvision.)
12. Languages. "Your ability to speak... is limited to the capabilities of your beast form." (Wild Shape) But as your mental stats and "personality" aren't changed, I think it's fair to say you still know your languages.
13. Challenge. Moot, but in case you care, you now have a CR.
14. Special Traits. You've got 'em.
15. Actions. You've got 'em. (Including, as was recently asked, Multiattack.)
16. Reactions. Sure.
17. Limited Usage. Yup.
18. Equipment. Beasts don't come with equipment. But if they did this'd be a weird one....
19. Legendary Actions, Lair Actions, Regional Effects. Not assumed, per Wild Shape.

"You retain the benefit of any features from your class, race, or other source and can use them if the new form is physically capable of doing so." (Wild Shape)

Alert

You gain a +5 bonus to your initiative. You can't be surprised while you are conscious. Other creatures don't gain advantage on attack rolls against you as a result of being hidden from you. (PHB p.165)

Okay, my beast form is definitely capable of taking advantage of all of those. For initiative I now look at my beast's DEX modifier, add +5 from Alert, and that's my initiative modifier.

Lucky

You have inexplicable luck that seems to kick in at just the right moment. [The mechanism by which we game-play that luck.] (PHB p.167)

My beast form is lucky. Cool.

Some other examples:

Inspiring Leader (targets need to see, hear, and understand you) will likely be a hard sell. Mounted Combat's another one.¹ But Mobile and Savage Attacker should work just the same. For that matter, so does Great Weapon Master: note that MM at pp.10-11 specifies that (most) monsters' melee attacks are weapon attacks, even those with "a natural weapon, such as a claw or tail spike."

Ability score increases borne from feats, however, are replaced by beast statistics, as Miniman's excellent answer to that linked question explains.

¹ Contrary to what most people say, the most dangerous animal in the world is not the lion or the tiger or even the elephant. It's a shark riding on an elephant's back, just trampling and eating everything they see. -Deep Thoughts, Jack Handey