First time investing. Have four children 6 and under. I wish to start putting money aside for them to go to college (or other things that might come up, like marriage, etc.). One idea I have: instead of opening one 529 for each one of them, why not open a general purpose account with Fidelity or the likes, under my name, and start putting money on mutual funds. As they each need the money, I can write the checks accordingly. Please help me think through the tradeoffs of having multiple specific accounts vs one broad one.
Morrison Changs's answer is very good I would like to add a few additional points.
You have 4 children 6 and under. One main benefit of many 529 plans is that they have an age based plan where the investments become more conservative. In fact the Utah age based plans let you pick from 4 different age based plans (Aggressive Global, Aggressive Domestic, Moderate, Conservative). Those age based plans automatically move along a glide path to become more conservative as the child approaches the start of college. If you tried to use funds from one account to help children 5 years apart the fund would be too aggressive for the child in college or too conservative for the child in middle school. Imagine if all the funds were in aggressive investments this year and a family had 1 or 2 of the 4 kids in college.
My interpretation of your question is that you are thinking of using Non-529 accounts. That would make the ability to create an age based account expensive. You could have to pay taxes as you sold shares in the aggressive fund so you could purchase shares in the more conservative fund.
The fact that the funds grow tax deferred in the 529 plan, and that if the funds are used for education the growth is then tax free can make a big difference in home much tuition you can purchase.
I would make 4 funds for reasons as described in the other answer I linked to. An argument for one large fund is that it is hard to predict how much money they will need. But one argument for 4 funds in the 529 plan is that you can move money between the 4 accounts. So if you have left over funds in the older child's account when they graduate, you can move the funds to the younger children's account. I have done that.
A wrinkle I didn't appreciate until the events of this year, is that if you receive a refund in tuition you can put the money back into the 529 plan. Many students this year received refunds because of the cancellation of classes or the switch to online learning. Their parents can put the refunded back without tax implications.
In your question you mention that you will also be saving for non-education things such as weddings. That is great, but there are tax implications if you want to use the 529 plan funds for non-education expenses. So you will have to decide how to split your savings between non-education and 529 accounts.
From my reading of the Utah 529 Plan - My529.org
I don't think you can consolidate your children's 529 into a single account.
Normally each account has to have only one beneficiary (child). As qualified educational distributions will need to have the appropriate beneficiary tax id. Trying to change beneficiaries is actual paperwork submitted to the plan. If the children had a large age gap that may work, but having multiple children in college at the same time actually makes it more cumbersome (if not impossible) if the 529s aren't separated.
In Utah, there is a per qualified beneficiary Utah state tax benefit for the owner (parent) of 5% of the single/joint contribution up to $2040/$4080, See: page 2 of March 27, 2020 Supplement. So having 4 children means that you can, depending on your tax filing, contribute $2040/$4080 per child. You are still free to gift up to the Federal tax limit without issue, but won't benefit the account owner at the state level.
In Utah for a beneficiary to be qualified, that person needs to be younger than 19 when the account is created. Utah state income credit/benefit can be revoked on future contributions if there is a beneficiary change to one 19 years or older. See: Utah 529 Program Description July 11, 2019 - Utah State Tax Considerations - Age Considerations p.60
One thing to look into is that Utah based corporations/flow-thru entities are also eligible for Utah Income tax benefit per the March 27, 2020 Supplement. This feels like something aimed at small business owners as I'm not sure who wants a "corporation" as the owner of your child's college fund.
While the income tax benefit is relatively small - 5% of contribution, Utah is allowing for a number of stacking behaviors which you wouldn't get with just a regular savings account/brokerage account. But you are limited to the fund selection for Utah's 529.
Further discussion about multiple children can be found: 529 (college saving) account for multiple kids