The IRS doesn't limit the amount you can invest in a traditional IRA based on how much you earn. Instead, phased removals determine if your income prevents you from requesting a full tax deduction for your traditional IRA contribution. No, there is no maximum income limit for a traditional IRA. Anyone can contribute to a traditional IRA.
While a Roth IRA has a strict income limit and people with incomes above it can't contribute at all, that rule doesn't apply to a traditional IRA. Tax-advantaged retirement accounts, such as traditional IRAs and Roth IRAs, are structured with specific tax advantages, such as the ability to make pre-tax contributions and benefit from tax-free growth. You may still want to make a non-deductible contribution, either because you prefer to allow your investments to grow tax-free and defer income taxes or because you want to make a clandestine contribution to a Roth IRA by contributing to your traditional IRA and then converting it into a Roth account. A spousal IRA allows both spouses to maximize their contributions to the traditional IRA, even if one spouse doesn't work or has very little qualifying income.
Traditional IRAs don't have this rule, as do other types of IRAs, such as SEP and SIMPLE IRAs, which are often used by self-employed individuals and small business owners. The ability to make non-deductible contributions regardless of income level makes traditional IRAs a valuable retirement savings account that can be converted into a clandestine Roth IRA.