Your objections are entirely reasonable and the attorney is going overboard with caution and penning you in when you aren't legally bound, perhaps in the hope of avoiding hurt feelings among potential clients, or to avoid creating a conflict of interest for the attorney.

> can a trust be written that grants powers to a trustee that are
> sufficiently broad to allow the trustee to make distributions of
> principal and interest to beneficiaries on an as-needed basis?

This is allowed and indeed is common and routine. A requirement to make distributions equally would be the exception rather than the rule.

> Of course, that would require that exquisitely detailed records be
> kept to track the percent ownership of various assets, but is there
> anything in estate law (or IRS rules) that precludes this?

Regardless of what the trust allows, you must keep detailed records of what is distributed to whom, when. But, you have no obligation to keep track of percentage ownership of various assets so long as you have this discretion which it appears you do. You don't need to keep track of that because you have no duty to treat everyone equally.

For income tax purposes, you are managing what is called a "complex trust". In a complex trust, you first calculate total trust income. Distributions are treated as if they come first from income and then from principal. They are taxable to the person receiving them to the extent that they are from income. Undistributed income in a given tax year is taxable to the trust on form 1041, not to any beneficiary and once taxed becomes principal for income tax purposes. 

There are moderately complicated rules to decide which kind of income is taxed to whom if the trust has more than one kind of income in a given year (e.g. partially taxable interest, partially tax free municipal bond interest, and partially long term capital gains), that an accountant can help you figure out.