In these three Legend Lore articles Mike Mearls talks about the fact a major design goal of D&D 5e is to Unite the editions.Specifically allowing the core game to be modified to play similarly to one of the past editions of D&D.
Uniting the Editions
While not all mechanics were carried forward from past editions, vancian magic was one of them. Vancian magic in a modified form with at-will cantrips, prepared spells, and rituals. The most direct answer to your question magic is what it is because that how it was presented in OD&D, AD&D 1st, AD&D 2nd, and D&D 3rd. It was modified in light of the experience with D&D 3e and D&D 4e and for reasons outlined in this article.
I could leave the answer like this but I feel it not complete. Some will wonder why Vancian magic in the first place?
It started, like in many mechanics in OD&D, with Chainmail. By the 2nd edition of Chainmail, wizards of varying power were introduced in the fantasy supplement. The four levels were Magician, Warlock, Sorceror, and the most powerful the Wizard. The difference between the different levels was not only in the power of their spells but the number of times per day they could cast spells.
When Gygax developed his Greyhawk Campaign he decided not to use Dave Arneson's system of magic reagents but rather was inspired by Jack Vance's Dying Earth series to create the familiar mechanics of spells in a spell book and the magic-users memorizing a limited selection of spells from the book.
This is corroborated in both Jon Peterson's Playing at the World and Kent David Kelly's Hawk & Moor series.
The mechanics are designed in 5e to reflect the spell memorization of classic editions of D&D which were inspired by the literature that Gary Gygax read most importantly Jack Vance's Dying Earth which were adapted from the Fantasy supplement of Chainmail which was used by Dave Arneson in his Blackmoor campaign.
DnDBeyond is probably the best solution
DnDBeyond is WotC's official digital location for rules and material for 5e. However, you must purchase any material that is not part of the Basic Rules/SRD in order to see details from that source. However, it has search functionality that seems to meet your exact needs.
By going to the magic item section and selecting "advanced search" you can do searches by many different parameters. Here is an example search for items that do fire damage.
The search results will show you a list of all items that meet your search criteria regardless of what you have purchased digitally. But you will only be able to see the details of that item if own that digital source. You can actually buy just that item from the source if that is all you are interested in as well.
Best Answer
The designers put their reasoning right in the DM Guide. Experience Points are now optional to help make the game work with more styles of play.
(DM Guide, page 261)
To support playing without experience points, you can't have a mechanic that requires them, or an economy that uses them.