Why do SPACs issue units instead of shares and warrants only?

They issue units because when they are fund-raising they lay-out the terms on how much a certain amount of investment is convertible into shares/warrants. So for starters, it is a generally easier negotiation i.e. you will get 1 share + 1/4 warrant per unit at $10 per unit investment. Moreover, it also sets the terms in a more simplified and easily calculated way... $10/unit is easier to split up in 100m units for example than say $9.75 per share + $0.25 per 1/4 warrant.

Also, similar to the point on easier negotiation, the terms for each SPAC presented in the S-1 is different per each blank-check company. By selling units at $10/unit, it standardizes the process where some SPACs can offer 1/3 of a warrant attached... no warrants attached... 2/9 attached etc.

Lastly, by selling units to the subscribed investors thus attaching warrants to shares, it incentivize the institutional investors to get in early and help fund the SPACs IPO. Basically giving the institutions an advantage and edge on getting in early, because why would they subscribe to the IPO for only shares for example, when they could hope some other institution or investor steps in and they just buy them on the secondary market days or weeks later. Also, remember: the units are not redeemable, the shares are - by letting the early subscribers in early they are able to have a guaranteed arbitrage of sorts.

Here are some interesting links for your reference:
SPAC Presentation from Winston & Strawn LLP
PwC Insights on SPACs
What You Need to Know About SPACs -- SEC
CFI (Corporate Finance Institute) on SPACs