Why can't a string ( or something ) be tied around a fractured Maxillary-first-premolar, so that natural remineralization will may occur?

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Why can't a string ( or something ) be tied around a fractured Maxillary-first-premolar, hopefully fitting the fracture together properly, so that natural remineralization will may occur ?

• Maybe the Maxillary-first-premolar starts out like two separate teeth and then natural mineralization occurs and they join to become one tooth, I obviously don't know.
• Two or three years ago I insisted to a dentist that they greatly reduce the very prominent inner cusp on this exact fractured Maxillary-first-premolar ( PM1 ), because I was very afraid that this exact thing would occur, from noticing how sometimes it would accidently knock very dangerously against lower teeth, but the dentist refused saying that taking away valuable tooth material is wrong.
• I have noticed that when i keep the broken inner cusp ( free moving cusp ) of this Maxillary-first-premolar against the intact cusp, instead of sometimes wiggling it, that that seems to greatly reduce the episodes of gum inflammation ( lots of septic tasting fluid ) and more recently bleeding, the septic fluid and blood have lessened very very noticeably by doing that.
• I just cannot find any webpages of people ( DIY ) tying a string around their broken Maxillary-first-premolar, hopefully fitting the fracture together properly, so that natural remineralization will may occur, obviously I would not be the first to think of this.

 

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Referring to a fractured Maxillary-first-premolar, fractured right up / down the middle ( so that the inner cusp moves freely sideways ) that dentist say the only option is extraction of the whole Maxillary-first-premolar.