Why don't "buy uptick" and "sell downtick" orders exist?

Question

I am learning about tick-sensitive orders. I know that there are two kinds of tick-sensitive orders:

Buy downtick order: can be filled only on a downtick or zero downtick price.

Sell uptick order: can be filled only on an uptick or zero uptick price.

However, in Trading and Exchanges: Market Microstructure for Practitioners by Larry Harris, the following question appears as an exercise (chapter 4, page 88):

Why are there no buy uptick and sell downtick orders?

Indeed, why? I've been thinking about this for some time now, and I can really figure it out. As far as I can understand, tick-sensitive orders are not replaceable with regular limit orders or market orders, so why don't "buy uptick" and "sell downtick" orders exist?

Flux · Answer

Why are there no buy uptick and sell downtick orders?

I think the textbook is looking for this answer:
These order types increase volatility, which is undesirable. If buy uptick orders were widely used, a single uptick could cause a huge cascade of buy orders, which could cause the price to rise more than it would without such orders. Similarly in the other direction for sell downtick orders.

Why don't "buy uptick" and "sell downtick" orders exist?

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