Sorry, but your assumption is wrong. Verdana
(verdana.ttf, version 5.05 with 191,344 bytes) has a very limited list of supported characters, i.e. the number of glyphs is quite low with 1391 glyphs in version 5.31. Courier New
(cour.ttf, version 5.13 with 711,092 bytes) with 3458 glyphs in version 6.80 and Arial
(arial.ttf, version 5.22 with 774,236 bytes) with 3988 glyphs in version 6.80 support much more. Most Unicode characters are supported by Arial Unicode MS
(arialuni.ttf, version 1.01 with 23,275,812 bytes). The number of glyphs is not specified on Microsoft's documentation page for font Arial Unicode MS, but the font file size of more than 22 MiB is a strong indication that this font really supports many characters in comparison to most other fonts in Windows fonts directory with a file size lower than 1 MiB.
It can be seen with UltraEdit for Windows v220.127.116.11 running on Windows 7 SP1 that the font Verdana does not support most
characters of the UTF-8 with BOM encoded file (basic status bar).
It can be seen with UltraEdit for Windows v18.104.22.168 running on Windows 7 SP1 that the font Courier New does support all
characters of the UTF-8 with BOM encoded file (standard status bar).
But why are all characters displayed in Windows Notepad as expected on using font Verdana?
Windows Notepad does not use font Verdana for all characters. For each character not supported by Verdana a different font is used which supports this character. That is a Windows feature available for all full Unicode aware applications.
UltraEdit for Windows is since v24.00 also a full Unicode aware application. So UltraEdit v25.00.0.68 with Verdana configured as font for document window area displays also all characters correct although font Verdana does not have glyphs for most of the characters in the UTF-8 encoded file.
Here is a screenshot that I made from UE v25.00.0.68 with the UTF-8 encoded file opened and with my preferred bitmap font Dina configured. Dina is available only in the font sizes 8, 9 and 10 with a very limited list of supported characters.
Dina is not installed with Windows. I have downloaded and installed this bitmap font manually. I have configured a much larger font size as this bitmap font supports to clearly see the difference. The first 8 characters are supported by Dina. For that reason the font rendering engine of Windows takes the bitmap and enlarges the bitmap to required size resulting in a square look. The other characters are displayed much better. The reason is that those characters are displayed using glyphs of font Arial which is a vector font which can be scaled to any font size smoothly even unusual font sizes like 24.39 points.
Internet browsers do in the meantime the same. If the font as defined according to HTML and CSS does not support a character to display, a Unicode fall back font is used for this character to display the character nevertheless correct. This approach has advantages and disadvantages as always when an application auto-corrects something for the application's user. A user thinks that Verdana supports all Unicode characters and it must be a bug of an application if getting characters displayed with default glyph as defined inside the font for a not supported character. Web authors do not recognize that for some characters it would be in real necessary to add a SPAN element and specify a different font for the character(s) enclosed by the SPAN than the font usually used for the text.