EA drops a ton of SP content for MUT. According to EA the majority of MUT players don't play H2H.
There are Theme Builders solos which let you play up to 10 team's regular season schedule. The games are short: they start at 3 min quarters and work their way up to 5 as the "season" progresses. You will unlock more of these as you level up. If you try it make these an early priority as you can both continue to level up and get awesome (and free!) players for your team.
Also each week EA drops 13 full game challenges in the Solo Battles mode. Once your team is good enough to contest All-Madden you'll be able to enjoy the most challenging SP experience the game has to offer, so long as you don't cheese the CPU.
Edit - The Legends solos are also full games and give much better coin payouts. You also get a free PU player that you can either add to your team or sell at auction for even more coins. Some of the Legends are LTD, that means they are only available for a limited time. Once their solos expire the price of the power up card explodes on the auction house, so if you wait to sell you can get a nice little payday for winning a single game.