To offer a counter-example, I just sat down with some kids to use these new rules to make new characters. The actual character creation was a disaster (not due to rules, but due to specific individuals who showed up and did not mesh well) but just about everyone made mixed race individuals. Here is what I remember without looking at their sheets.
Tiefling/Dhampir -> Wanting to play a very edgy character, who feeds on emotions and has devilish ties. Works perfectly.
Water Genasi/Aasimar -> Wanted to be the child of a water deity. Works perfectly.
Tabaxi/Kobold -> Wanted to be small, fuzzy, and connected to a dragon (some homebrew lore on how Dragonborn and Kobolds work). I could probably literally find artwork of small, fuzzy dragons in a 10 second search. Works perfectly.
Tiefling/Dragonborn -> Wanted to combine fire and ice characteristics, and have a connection to dragons as well. Works perfectly.
And honestly, even the OP's stuff, that is intentionally choosing to not present any features of one of their parents. The halfing that breathes fire may be "silly" but they are immediately less so if they looked like this
View attachment 261080
Which seems to be art of... a halfling half-dragon. Which is what someone who makes a halfling/Dragonborn character likely WANTS.
Sure, you can make a dwarf who flies by flapping their arms. But that is entirely on you for making the character to be silly. A dwarf with wings is likely what an actually player taking this seriously would do. Which is such a common idea there are minis for it.