Should one capitalise the first word in the body of a letter?

From Great Grammar Practice Grade 2 copyright 2015 Scholastic Teachables. Here it is demonstrated in one reference book. The exercise shows what letters need to be capitalized, including the first word of the first sentence after the greeting.

Dear Uncle Alex,
Thank you for the book you sent for my birthday. I have wanted to read it for a long time. Now I can!
Your niece,
Sue

From Good English Form Book in Business Letter Writing, 1904 another source dictates (p. 17):

Begin every sentence, line of poetry, or formal quotation with a capital. NEVER USE A CAPITAL LETTER UNLESS YOU HAVE A REASON FOR IT.

The book is accessible for free at archive.org with ample exercises and examples. I am concerned that these two authorities might offer only for preference of style, but it is the same in regards to capitalization after a greeting in the body of a letter.

In a comment, EdwinAshworth mentioned these sources as well, which may prove more helpful, so I include:

Letter Writing Guide, Reading Rockets, and the Centre for Academic Success (which capitalises a phrase!) all use/require the capitalise-the-first-word-after-the-salutation convention.

Dear Recipient is a salutation, it is not part of the following text. Thus, it is set off above the content of the letter and followed by a comma in less formal communication.

In business formatting, the salutation (e.g., Dear Sir) is followed by a colon.

I was taught this in engish class, " Dear Sally, How are you? " This is correct to me.

I remember having been taught (in my English class in school in Wales) that as there was a comma after the persons name, the the first letter of the first line of the first paragraph was not capitalised as it came after a comma.