If you have plenty of other capital to deploy, and paying down that loan a bit quicker isnt going to keep you from continuing to invest in other avenues, then I don't see a major downside.

This has the downside of not being taken seriously. 

Its pretty much instantly in your account.....A lot of people use Cozy and other third party companies...... the downside is if you use the free service it takes days for you to actually have the $$ and the tenant can lodge disputes and "reverse" the payment through those services.... then you have to fight to get the $$ etc......

Thats one of the down sides of buying into coops.

Are there any additional downsides to the conventional loan vs FHA? 

However, it's important to consider the potential downsides, such as the need for frequent turnover and management tasks, and the potential for seasonality or market fluctuations.

I buy 1st and pay between 7-9% with little risk.The only downside with this investing is you give up depreciation.  

DOWNSIDE; turnover costs can be high and take a long time to make that up(2) Increase it but keep it a decent % below market.... keep the tenant, avoid turnover costs that can take years to recoup.

So over the course of 6 months to a year, you've just bought a house for no money, but the downside is you have to tie all that money up for that period of time.

The longer rates stay high the greater risk of downside surprises.