[Turtle91]

I've always used blockquote when it is a longer quote...typically two or more paragraphs. I think that is why people are used to using the <p> tags inside of a blockquote. If it was a single paragraph then it's easier to just style the individual paragraph:

p.quote {margin:1em; text-indent:0; text-align:left; 
         font-size:.8em; font-style:italic}

<p>This is a normal paragraph before the quote.</p>
<p class="quote">Yadda yadda yadda...</p>
<p>This is a normal paragraph after the quote.</p>

vs.

blockquote        {margin:1em auto; width:50%}
blockquote p      {margin:0 0 .75em; text-align:left; text-indent:0; 
                   font-size:.8em; font-style:italic}
blockquote p.auth {margin:1.5em 0 0; text-align:right; font-style:normal}
blockquote + p    {text-indent:0}

<p>This is a normal paragraph before the blockquote.</p>
<blockquote>
  <p>Yadda yadda yadda...</p>
  <p>Also, yadda yadda yadda...</p>
  <p>But then, yadda yadda yadda...</p>
  <p>Finally, yadda yadda yadda...</p>
  <p class="auth">- Dion, circa 2022,<br />post pandemic</p>
</blockquote>
<p>This is a normal paragraph after the blockquote.</p>

I only use classes when there is something different about that particular thing...otherwise I simply define the base tag...that keeps the code view nice and clean, reducing bloat. It drives me nuts when I see things like this on every paragraph:

<p style="margin:0.00% 0.00%; text-indent:1.2em; text-align:justify; widows:0; orphans:0"> <span style=" font-size:1.0rem">Hello.</span> </p>

when it could be just:

p {margin:0; text-indent:1.2em}

<p>Hello.</p>