I cannot see any particularly problematic spells, but stopping at 5th level fits the tiers of play and general trends in the rules
The section of the rules on Tiers of Play states:
The shading in the Character Advancement table shows the four tiers of play. The tiers don’t have any rules associated with them; they are a general description of how the play experience changes as characters gain levels.
[...]
In the third tier (levels 11–16), characters have reached a level of power that sets them high above the ordinary populace and makes them special even among adventurers. At 11th level, many spellcasters gain access to 6th-level spells, some of which create effects previously impossible for player characters to achieve. Other characters gain features that allow them to make more attacks or do more impressive things with those attacks. These mighty adventurers often confront threats to whole regions and continents. [...]
There are other parts of the rules that follow this same separation, such as the optional Spell Point Variant rule which states:
[...] Spells of 6th level and higher are particularly taxing to cast. You can use spell points to create one slot of each level of 6th or higher. You can't create another slot of the same level until you finish a long rest. [...]
A sorcerer also cannot create spell slots of higher than 5th level using Flexible Casting. We can also see that warlock spell slots stop at 5th level, that is, they do not suddenly get short rest refilling 6th level spell slots.
Another example of avoiding granting too many higher level spell slots is the Ring of Spell Storing. It cannot hold spells of 6th level or higher.
Another thing is that when a regular caster gains their first spell slot of level 1-5, their very next level grants them another one. In contrast, spellcasters never get more than one 8th, or 9th level slot and only get an additional 6th level one at level 19 and an additional 7th level one at level 20.
Finally the Boon of Spell Recall and the Boon of High Magic are two of the only ways to get additional higher level spell slots and they are both Epic Boons, an optional post-level-20 progression method.
So while I can't think of any exceptionally alarmingly good uses out of casting two 6th level spells (after all, this can be done at level 19). I think effectively giving this ability can be dangerous since it lets the wizard get well ahead of other spellcasters and the developers believe spell slots of 6th level and higher are very powerful.