Honestly, the centre channel for HT is highly over-rated and un-necessary in typical setups. Most people don't have an acoustically transparent projection screen and their mains and centre aren't identical and mounted where they should be (i.e. up and in line behind the screen). Like this:
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People have their flat panel above the centre channel speaker and the LR mains higher up. All the imaging realistically comes from the mains and if your mains are fantastic imaging speakers you can sit anywhere and the phantom image is still more than good enough, even when off centre. Main reason, the phase information even in discrete digital multichannel is backwards compatible with the good old analog way of doing it- a mixdown to phantom or even 2.0 will give you a glorious L-R stage, two speakers and no crap speakers littering your room.
That's the way I do it, we dispensed with centre speakers and HT years ago. I use the various centres now as sacrificial speakers for my test bench.
Many years ago I had 8 identical large three ways (2 centres), a pile of big power amps and although impressive, I just got sick and tired of surround in general. It's so done and so boring. I guess that comes from selling the stuff and "helping" far too many friends with their "custom install home theatres" which ranged from the tackiest hollywood inspired fiascos to "converting" a bedroom into a HT. Fixing up rubbish installs by professionals, crawling through roof spaces and running cables. Making wall plate after wall plate for my "friends" etc. I'm really glad the HT craze is long gone, now it's fire-pits, pizza ovens, collaborative tech spaces and designer butler's kitchens.
So, no, you don't need a cheap ass centre speaker. Either go hard or go home. Get identical LCR large full range speakers if you must do it.