You are correct in your original assumptions. However, if you pay a partnership or single proprietorship on W-2, you create a sitatuation where they may actually pay more tax, and the LLC may end up paying tax on those earnings as well...sort of like double taxation. This is one of the reasons the LLC form of corporation was created.
When you pay shareholders on W-2, you are treating this as a C corp or as an LLC which has elected to be taxed as a corporation. The C Corp model is to pay corporate officers on W-2.
Its not all the income that passes through, it is the NET Profits that pass through. The partners only pay self employment tax on the net profits.
For an LLC single proprietorship or partnership, the W-2 is not appropriate because it creates a situation where some of the revenues are double taxed, and a sitaution where soem of the share holders have more complicated tax returns. They have already had the employee share of the ss tax withheld, and the LLC would have paid the employer contribution, now on the shared earnings not included in W-2, they have to pay se tax on the passed through profits.
The final word is that the IRS states that partners can not be treated as employees being paid on W-2. Because of ingnorance and convenience, many LLC's are doing this, but it is incorrect. When audited the IRS will dis allow the treatment. Only in about 50% of the cases does a tax court rule against the IRS position in this matter.
This is all because many rules in the regulations are based on payroll. For example, manufactures and domestic production credits, to name just two.
The IRS collects more tax, if you treat partners as employees rather than if they are treated according to regulation as partners and owners who pay SE tax.
Rev. Rul. 69-184 that a Partner should not be treated as an employee for purposes of compensation.