Why participating preferences maybe absurd and how 409A valuations can consider this absurdity?

Imagine a term sheet where your pre-money valuation is $25million and you raised $5 million. The post money valuation therefore is $30 million and the VCs share of the company is 5/30 or 16.7%. Now, the liquidation preference (typically at 1X the investment dollars or issue price) would be $5 million and let us say the VC wants another 1X in participating preference. One of the interesting things to note is that the $30 million valuation is almost 6 times the liquidation preference ($5MM) and 3 times the participating preference ($10MM) thresholds. When analyzing the waterfall model, it can be shown that the full per share issue price of the VCs stock is reached when the valuation equals or just crosses the liquidation preference amount. Anything beyond this is a value that accrues to the preferred share price until the participating cap is reached at $10 million valuation. Given that the valuation right on the day of investment is $30 million, the VCs would have made money on their stock on the day of investment, and then some, as the valuation would have crossed even the preferred participating threshold. And, if the issue price is set in a certain way that the VCs would find it in their interests to convert to common stock, then even more money would accrue to the per share price of the VCs, right on the day of investment. Note that this money is only on paper and no worthwhile progress toward creating or meeting milestones has been made by the target company. The valuation conundrum leads to the creation of artificial wealth. Whew, talk about magic money.
On the other hand if the valuation was just restricted to the liquidation or participating preference caps, then the VCs would end up owning all the shares in the company - a non-viable proposition as well.
This is one of the reasons we do not take VCs post money valuation as the sole indicator in 409A valuations. We even go as far as to term this "investment value" - a notation that can be given less weight under 409A valuations, or some times, depending upon the investment conditions, completely ignored.

When negotiating term sheets, should a founder just focus on anti-dilution clauses?

Many founders are focused on whether or not to include anti-dilution clauses. What they fail to realize is that the funding structure is more complex than just dilution. A VC can invest in a way that it may look like you are holding 50% of the company's common stock, but you may get allocated a much lesser value. For instance, if the VC negotiates a 2X liquidation preference with a full participating feature with a cumulative dividend pay out of 8% per year (and barring dividends to be paid to the common stock holders), the common stock despite having a 50% position may in reality get less than 10% of the company's value at exit. They can also add warrants that currently wont dilute common but on exercise will (it is just a delay effect - makes the founder's stake larger than it actually is). All this mean your stake has been effectively diluted through a variety of means and not just direct dilution. We use random scenarios to prove what a founder will get in different negotiating situations. There are also pay-to-play clauses which also affects common stock value. If you have anti-dilution protections in there, the VCs will simply negotiate a stricter participating preferred stock. The only way to negotiate is to go in with a game theory based model and keep plugging in VC numbers in a Monte Carlo random simulation scenario to see if the founders have a decent RoI under a random exit scenario.

I strongly advise that founders consult with experts like us to see if VC terms are fair game. We can calculate this using prevailing peer volatility considerations. If you are returning a VC more than the average return a VC expects, you are really not negotiating very well. We have reviewed so many SPAs where dilutions have been achieved through several creative terms. The VCs are good at this - they have analysts on their side. Founders need to get someone on their side as well.

We know of companies where the VCs had so many clauses that founders had to renegotiate their stakes when they realized that, in the middle of their  company's development, they wont even get 1% of the return. We had to go in and create a new preferred security class for the founders instead of the usual common stock, just to keep the RoI fair and the morale high.

Series A and Series B term sheet negotiations are critical to realize a fair RoI the founders. Fortunately, today, we have decent models to do this.