Besides the valuation aren't we heading into (or already are in) a situation that as bond rates rise, more people will invest in them instead of stocks thus causing stocks to drop further? And the more stocks drop, unless rates drop, more people will continue to move money into bonds?

While 5% interest isn't huge, it is likely to gain you a real return (although small) which for many is sufficient as compared to the risks many see in the stock market. I know there are others who aren't afraid of stock market drops but many investors are. Throw in TIPs that are providing 2% or more above inflation many may prefer safe returns than watching money drop in the market.

Of course now I see on other forums people panicking and running away from bond funds since they were under the illusion bond funds are safe and wouldn't lose them money and now seeing a 15-20% drop is causing them serious heartburn.

I've rarely ever owned bond funds and usually just own stocks/ETFs and cash. Since I recently retired I have most of my money needs in various treasuries (owned directly and not via any funds) to cover the next decade and my other account mostly in stocks or a guaranteed income fund (roughly 90/10).