Using words like 'forcing' and 'penalising' will work in the opposite direction to what you might hope.
You already identify the issue - full time workers require benefits and the like. For many small organisations, these make the cost of a full time worker prohibitive, so they fill in with multiple part time instead. The employer is incentivised to keep people part time.
The danger is real. There are very few activities which can't be done remotely today, other than... massage, food service, medical (but even then some can be outsourced, e.g. radiology).
I would prefer to see positive incentives, e.g. a tax break for every full time job that is filled domestically. Give them a financial reason to hire full timers, and they'll hire full timers. Punish them for hiring part timers, and they'll just move overseas, and then another few million people will be permanently unemployed or under employed.
This goes towards the "good job" / "American Dream" aspect of the article. People shouldn't have to work 2 or 3 part-time jobs to make a living if they don't want to, just because those are the jobs available. If somebody wants full-time employment (for which they are otherwise qualified), it would be better for them to have that.
Of course, it is cheaper for the corporations to use part-time, because it keeps them flexible with scheduling/substitutes and due to added costs like benefits etc.
I have been trying to figure out whether it makes sense to offer tax incentives/penalties which would push the balance towards more full-time jobs instead of part-time. One piece I have envisioned is forcing employers to offer the benefits a full-time employee would receive prorated to part-timers, with a penalty added for splitting it up. Make them want to offer a full-time job instead.
The part I am worried about is whether the effect is too strong and prevents somebody who actually only wants part-time work from finding employment (e.g.: a student, full-time parent, senior citizen or handicapped person). There needs to be some part-time work available, but generally a member of the workforce probably wants a full-time job.