Bad assumption, at least in my area with my soils. If I follow best practices for establishing clover by fall planting with a winter rye cover crop after a good burn down and followed by timely mowing the first spring to release the clover, I'll get a great plot with no herbicides. Weeds will begin creeping in slowly in the next year but it takes quite a while before the percentage of weeds is great enough that I need to rejuvenate or rotate. If I try to establish clover in the spring, weeds will take hold. Once they take hold, my warm season weeds are hard to get rid of. Even if I seemingly clean the field with herbicides, those weeds come back much faster. I spend more money and time trying to deal with them.
I want to add one more thing. When I first started, I spent a lot of time and effort trying to keep clean clover fields. I've learned over time that while they look great, they really don't benefit my deer more than a weedy field (given my objectives and techniques). In fact deer eat many of what most consider weeds and they can be as or more nutritious than the clover. The weeds also help shade the clover in the summer. Again, the practices that work very well in my area, may not be the best fit for you. However, I've found that when I establish a very clean field to start using best practices and then after the first year of establishment, ignore weeds and simply mow to release the clover once in the fall just as nights are turning cooler favoring the clover and fall rains are beginning to start, the clover bounces back very strong and provides a great fall plot even when it looks like crap in the summer. Eventually when the field gets weedy enough, I'll hit it with a quart of gly in late summer and drill radish through the clover. (Just posted a picture of that on another thread). This will give me a few more years out of the field but eventually clover needs to be rotated.
Keep in mind that in a field of waist high weeds, deer are often using the clover growing underneath. Also, I'm far enough south (zone 7a) that summer is more of a stress period than fall and I plant about 7 acres of soybeans to cover that summer stress period.
The reason I said "I'm guessing you'll spend more..." is that conditions could be different in your area. Summer weeds may not be as big of an issue as they are here. You field could have more clover in it than it appears from the picture. You can mow and see what happens this fall as you seem to have done. I'm just saying that based on my experience and your picture and description, I'd start over if it were me. This is a judgment call, not what is best in all cases.
Thanks,
Jack