Can't set default character size in Draw

In Draw if I don’t have anything selected and I change the font, that font will be used for all subsequent text boxes I create. This is what I want. However, if I change the font size, with nothing selected, the font size box will show the selected size, but whenever I draw a text box, the size will change back to the original size. As soon as I complete the text box the font size box switches back to the size I wanted (and set), but of course the new text box has the wrong size font in it. I got around this by creating a special style and template, but this is a lot of work just to set the default font size for a particular drawing. This inconsistency seems strange to me. Am I doing something wrong, or is there a bug in Draw???
LibreOffice Version:

A little more info: Writer lets me set the default font name and default font size by merely going to the standard toolbar, pulling down the font name or font size icon menus. It will then use that font and font size for text I type in until I change it. This behavior is exactly what I want to do in Draw.

Defaults are controlled by default styles in LibreOffice. For a long time the defaults for Draw were hard coded, but (at least) since V6.0 the default styles are accessible via >Format>Manage Styles or F11 or similar (in the SideBoard). You can modify default styles, and also create your own styles.
If you want a changed default or an additionally defined style to be inforce/available when you create a Draw document next time, you need to store and manage a respective template.

Thanks for the response. Using styles to set font sizes for a few text boxes is quite awkward. For one thing I must to have a style for every font size (hundreds). I would like to be able to easily set the default font size for a few text boxes, then change it for a few different text boxes.

I can hardly imagine a drawing needing to use hundreds of font sizes. Nonetheless there seems to be a case.
There also are cases where a general purpose software has no feature a specific user would dream of because he is in a very special situation.
Since the shape object “TextBox” and the text object it contains are basically merged in LibreOffice, I cannot think of a solution for your problem without relying on user code - and even such a solution might be rtather complicated or probably instable. You would need to register a listener for the creation of shapes, and a routine applying memorized attributes to the new shape (its text). The routine memorizing new attributes when ordered should be simple then.
However, I don’t even know if there actually is a “CreateShapeListener” (or the like) object.

The styles are the most valuable feature of the LibreOffice. Use them.

Create sample text with desired formatting and place out of the way on the document.
Click on it to Copy, Paste. Move the pasted copy to the desired location.
Original will stay for next use.

The real solution is to create a user style with all the preferred defaults. Or to customise existing styles, notably the default one. Since styles are saved in the user profile, changes will persists across sessions.

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@Lupp and @ajlittoz told you about styles which I would prefer.
For cases like yours the gallery could be helpful. Create a new theme with different samples you need. Everytime you need a little alteration you could implement it and then additionally set a sample object into the gallery. More information in the Draw Guide 7.3, page 273ff.
Note: Objects in the gallery remain and can be used in any newly created document (Draw; Writer…).