Take me to dumb school....Investment Property Equity

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I'll keep in brief. What is the general philosophy regarding paying off an investment property?

I'd really like to hear the opposing sides. More equity means lower payment and higher monthly cashflow...my beer math tells me that. Somehow I feel that sitting as equity is not the best use for the capital. Is it common to refinance regularly to pull out as much liquid or possible? Do folks even regularly hold on to paid off investment properties?

I'm curious to learn thanks.